Despite current moves in the UK to limit class sizes for young children in school, there is still a disturbing lack of research evidence on the effect of class size differences on pupils' educational progress and experience. Past research has concentrated on the effects on outcomes such as pupils' school attainments in basic areas. Much less is known about classroom processes that might mediate any such effects, though such knowledge is more useful for practice and policy. Drawing (...) on a current programme of research at the Institute of Education, University of London, this paper identifies five processes likely to be connected to class size: within class grouping practices, the nature and quality of teaching, pupil attention in class, pupil adjustment to school and effects on teachers' morale, stress and enthusiasm. Relevent research is reviewed, and in line with this research the paper concentrates on the primary school years. (shrink)

We define a program size complexity function $H^\infty$ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in ${\{0,1\}}^\omega$ relative to the $H^\infty$ complexity. We prove that the classes of Martin-Löf random sequences and $H^\infty$-random sequences coincide and that the $H^\infty$-trivial sequences are exactly the recursive ones. We also study some properties of $H^\infty$ and compare it with other complexity functions. In particular, (...) $H^\infty$ is different from $H^A$, the prefix-free complexity of monotone machines with oracle A. (shrink)

Agrifood scholars have long investigated the relationship between farm size and a wide variety of social and ecological outcomes. Yet neither this scholarship nor the extensive research on farmworkers has addressed the relationship between farm size and job quality for hired workers. Moreover, although this question has not been systematically investigated, many advocates, popular food writers, and documentaries appear to have the answer—portraying precarious work as common on large farms and nonexistent on small farms. In this paper, we (...) take on this question by describing and explaining the relationship between farm size and job quality for hired farm workers. To do so, we draw on data from two independently conducted, mixed-methods case studies—organic fruit and vegetable production in California, and dairy farming in Wisconsin—each of which offers a different set of insights into the farm size-job quality relationship. In both cases, larger farms fared better than or no worse than their smaller-scale counterparts for most job quality metrics investigated, though many of the advantages of working on large farms accrue disproportionately to white, U.S.-born workers. We explain that these patterns stem from economies of scale, industrialization, firm size itself, the dominant class identities and aspirations of farmers and their peers, as well as farmers’ and immigrant workers’ fears of immigration enforcement. (shrink)

This paper examines social network size in contemporary Western society based on the exchange of Christmas cards. Maximum network size averaged 153.5 individuals, with a mean network size of 124.9 for those individuals explicitly contacted; these values are remarkably close to the group size of 150 predicted for humans on the basis of the size of their neocortex. Age, household type, and the relationship to the individual influence network structure, although the proportion of kin remained (...) relatively constant at around 21%. Frequency of contact between network members was primarily determined by two classes of variable: passive factors (distance, work colleague, overseas) and active factors (emotional closeness, genetic relatedness). Controlling for the influence of passive factors on contact rates allowed the hierarchical structure of human social groups to be delimited. These findings suggest that there may be cognitive constraints on network size. (shrink)

For any Boolean Algebra A, let cmm be the smallest size of an infinite partition of unity in A. The relationship of this function to the 21 common functions described in Monk [4] is described, for the class of all Boolean algebras, and also for its most important subclasses. This description involves three main results: the existence of a rigid tree algebra in which cmm exceeds any preassigned number, a rigid interval algebra with that property, and the construction (...) of an interval algebra in which every well-ordered chain has size less than cmm. (shrink)

We study various aspects of the size, including the cardinality, of closed unbounded subsets of [λ]<κ, especially when λ = κ+n for n ε ω. The problem is resolved into the study of the size of certain stationary sets. Relative to the existence of an ω1-Erdös cardinal it is shown consistent that ωω3 < ωω13 and every closed unbounded subsetof [ω3]<ω2 has cardinality ωω13. A weakening of the ω1-Erdös property, ω1-remarkability, is defined and shown to be retained under (...) a large class of Easton-like forcings applied to ω1-Erdös cardinals. A class of reverse-Easton forcings preserving α-Erdösness is also described, with special attention to the establishment of □-principles. Article Outline. (shrink)

This article investigates the effects of firm size, profitability, industry affiliation, and the business cycle on retailer philanthropy. The importance of industry and firm effects on giving was analyzed with regression models using industry-fixed effects as well as firm strategy variables. The analysis included instrumental variables methodology to account for simultaneity in the charitable giving–profits relationship. Data were gathered from the IRS Corporate Statistics of Income Sourcebook, data that provide firm size class measures covering the entire firm (...) size distribution ranging from small retailers up to large multi-national retail firms. Retailer philanthropy was measured as the ratio of charitable contributions to total receipts. Important findings include a cubic relationship between retailer philanthropy and firm size; industry effects stronger than those observed for retail profit; and the absence of business cycle effects. The empirical research relating retail charitable giving to firm attributes including firm size and advertising, industry and business cycle factors are unique in the business ethics literature. Prior studies regarding the importance of industry on charitable giving utilized data across broad sectors of the economy. Firms from different sectors could be expected to differ in philanthropic approach due to differences in public contact as well as differences in public relations exposure. The strong industry effects reported for this sample of exclusively retail firms, with similar public contact, provide strong evidence for the importance of industry in determining firms’ charitable strategies. (shrink)

Elselijn Kingma argues that Christopher Boorse’s biostatistical theory (the BST) does not show how the reference classes it uses are objective and naturalistic. Recently, philosophers of medicine have attempted to rebut Kingma’s concerns. I argue that these rebuttals are theoretically unconvincing, and that there are clear examples of physicians adjusting their reference classes according to their prior knowledge of health and disease. I focus on the use of age-adjusted reference classes to diagnose low bone mineral density in children. In addition (...) to using the BST’s age, sex, and species, physicians also choose to use other factors to define reference classes, such as pubertal status, bone age, body size, and muscle mass. I show that physicians calibrate the reference classes they use according to their prior knowledge of health and disease. Reference classes are also chosen for pragmatic reasons, such as to predict fragility fractures. (shrink)

SummaryDate from the Census Fertility Reports are used to investigate social and regional variations in family size in the Republic of Ireland. Although Ireland is noted for its high level of fertility, average family size declined by approximately 10% between 1946 and 1971. There are distinct socioeconomic variations in family size in that Roman Catholic family size is greater than that of non-Catholics and the middle classes have the smallest families within each of the religious groups. (...) There are also marked regional differences in family size. In 1946, there was a clear division between the west coast counties with the largest families and the east coast conties with the smaller families. By 1961 and 1971 this pattern had become less clearly demarcated and areas with relatively large families were found in most parts of the country. It is suggested that regional variations in family size can be influenced by a variety of factors, such as differences in religious affiliation, occupation, infant mortality and the degree of selection through emigration. Of these factors, it is found that in both 1946 and 1971 variations in occupation were most strongly related to family size and it appears that economic and occupation changes within Ireland have brought about the changing regional pattern of family size. (shrink)

While sets are combinatorial collections, defined by their elements, classes are logical collections, defined by their membership conditions. We develop, in a potentialist setting, a predicative approach to (logical) classes of (combinatorial) sets. Some reasons emerge to adopt a stricter form of potentialism, which insists, not only that each object is generated at some stage of an incompletable process, but also that each truth is “made true” at some such stage. The natural logic of this strict form of potentialism is (...) semi-intuitionistic: where each set-sized domain is classical, the domain of all sets or all classes is intuitionistic. (shrink)

In this paper we consider classes of finite structures where we have good control over the sizes of the definable sets. The motivating example is the class of finite fields: it was shown in [1] that for any formulain the language of rings, there are finitely many pairs (d,μ) ∈ω×Q>0so that in any finite fieldFand for any ā ∈Fmthe size |ø(Fn,ā)| is “approximately”μ|F|d. Essentially this is a generalisation of the classical Lang-Weil estimates from the category of varieties to (...) that of the first-order-definable sets. (shrink)

A discussion of the philosophical prospects for basing a neo-Fregean theory of classes on a principle that attempts to articulate the limitation-of-size conception.

It is widely agreed that more is true in a work of fiction than explicitly said. In addition to directly stipulated fictional content (explicit truth), inference and background assumptions give us implicit truths. However, this taxonomy of fictional truths overlooks an important class of fictional truth: those generated by literary formal features. Fictional works generate fictional content by both semantic and formal means, and content arising from formal features such as italics or font size are neither explicit nor (...) implicit: not explicit since formal features don’t say anything; and not implicit since content generated from formal features doesn’t rely on other truths or background assumptions. In addition to showing that our current classification is incomplete, the new class of fictional truths provides four further upshots for definitions of fictional truth, story and work identity conditions, and the relationship between literary interpretation and fictional truth. (shrink)

This note is a continuation of our former paper ''Complexity of the r-query tautologies in the presence of a generic oracle.'' We give a very short direct proof of the nonexistence of t-generic oracles, a result obtained first by Dowd. We also reconstitute a proof of Dowd's result that the class of all r-generic oracles in his sense has Lebesgue measure one.

In connection with the work of Anscombe, Macpherson, Steinhorn and the present author in [1] we investigate the notion of a multidimensional exact class (R-mec), a special kind of multidimensional asymptotic class (R-mac) with measuring functions that yield the exact sizes of definable sets, not just approximations. We use results about smooth approximation [24] and Lie coordinatization [13] to prove the following result (Theorem 4.6.4), as conjectured by Macpherson: For any countable language$\mathcal {L}$and any positive integerdthe class$\mathcal (...) {C}(\mathcal {L},d)$of all finite$\mathcal {L}$-structures with at mostd4-types is a polynomial exact class in$\mathcal {L}$, where a polynomial exact class is a multidimensional exact class with polynomial measuring functions. (shrink)

This article aims to claim ‘body size’ as an increasingly important axis of signification. It draws on research from various disciplines to present an exploratory overview of the different ways in which body size categorizations – being fat or slender – intersect with other axes, such as gender, race, sexuality, social class and age. The article argues that an intersectional perspective on body size adds to our understanding of the layeredness and complexity of power differentials, normativities (...) and identity formations that co-produce inequalities. Furthermore, it attempts to show how processes of exclusion and marginalization based on body size categorizations are similar to racist, ableist and misogynist logics and practices. Hereby the article intends to demonstrate the vast impact of body size categorizations, specifically but not exclusively on the lives of those who occupy the marked position in relation to this axis: the ‘fat’. It argues that an intersectional perspective helps us to see body size discrimination more clearly and can help disrupt dominant discourses about the body in order to create a truly ‘healthy’ environment in which bodies of all sizes, shapes, colours and abilities can be celebrated. (shrink)

Let ZFB be ZF + "every set is the same size as a wellfounded set". Then the following are true. Every sentence true in every (Rieger-Bernays) permutation model of a model of ZF is a theorem of ZFB. (i.e.. ZFB is the theory of Rieger-Bernays permutation models of models of ZF) ZF and ZFAFA are both extensions of ZFB conservative for stratified formulæ. The class of models of ZFB is closed under creation of Rieger-Bernays permutation models.

As there are contradictions in the digital technology: 1) a tool for professional growth and 2) a tool for imposing a prepared scenario of achieving success on the subject, ignoring the principle of environmental compliance, our study aims to substantiate and experimentally test the effectiveness of the model of realization of modern student’s mental experience. Moreover, the technology of programming as philosophizing in the BSL format is considered to be an element in the humanization of geeks culture in the situation (...) of supposed technological singularity. In accordance with the goal, we have created a regression-correlation design for the study of the influence of the predictor variable on the criterion variable. The exploratory methodology of our experimental study is determined by the content of bite sized-approbation of the author's model ‘Flipped Class’. Its conceptual idea is self-learning as creativity, which is realized in the didactics of performative action. The results of the tasks have revealed the relationships and differences in the implementation of indicators of students’ mental experience of joint e-Learning and BSL, which are visualized in correlation galaxies for future clustering. They have confirmed the leading idea of ​​our study: the disclosure of the resources inherent in human nature in the process of learning is the way for the relentless cognition of the sense of placement with a view to achieving dignity and making free choices in life. (shrink)

We show that a $$ -simplified morass can be added by a forcing with working parts of size smaller than $\kappa $. This answers affirmatively the question, asked independently by Shelah and Velleman in the early 1990s, of whether it is possible to do so.Our argument use a modification of a technique of Mitchell’s for adding objects of size $\omega _2$ in which collections of models – all of equal, countable size – are used as side conditions. (...) In our modification, whilst the individual models are, as in Mitchell’s technique, taken ad hoc from quite general classes, the collections of models are very highly structured, in a way that is somewhat different from, perhaps more stringent than, Mitchell’s original, arguably making the method more wieldy and giving the prospect of further uses with more delicate working parts. (shrink)

This paper introduces a new Ehrenfeucht-Fraïssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating moves played in different models. The game allows Duplicator to delay her choices of the models till the very end of the game, making it easier for her to win. This adds on the toolkit of winning strategies for Duplicator in Ehrenfeucht-Fraïssé type (...) games and opens up new methods for tackling some open problems in descriptive complexity theory. As an application of the class game, it is shown that, if m is a power of a prime, then first order logic augmented with function quantifiers F1n of arity 1 and height n < m can not express that the size of the model is divisible by m. This, together with some new expressibility results for Henkin quantifiers H1n gives some new separation results on the class of finite models among various F1n on one hand and between F1n and H1n on the other. Since function quantifiers involve a bounded type of second order existential quantifiers, the class game solves an open problem raised by Fagin, which asks for some inexpressibility result using a winning strategy by Duplicator in a game that involves more than one coloring round. (shrink)

The purpose of this paper was to determine if quantitative rankings of highly cited research authors confirm Nobel prize awards. Six studies covering different time periods and author sample sizes were reviewed. The number of Nobel laureates at the time each study was published was tabulated, as was the number of high impact authors who later became laureates. The Nobelists and laureates-to-be were also compared with non-Nobelists to see if they differed in terms of impact and productivity. The results indicate (...) that high rankings by citation frequency identify researchersof Nobel class — that is, a small set of authors that includes a high proportion of actual Nobelists and laureates-to-be. Also, the average impact (citations per author) of Nobelists and laureates-to-be is sufficiently high to distinguish them from non-Nobelists in these rankings. In conclusion, a simple, quantitative, and objective algorithm based on citation data can effectively corroborate —and even forecast — a complex, qualitative, and subjective selection process based on human judgement. (shrink)

This research partially answers the question raised by Goncharov about the size of the class of positive elements of a Roger's semilattice. We introduce a notion of effective infinity of classes of computable enumerations. Then, using finite injury priority method, we prove five theorems which give sufficient conditions to be effectively infinite for classes of all enumerations without repetitions, positive undecidable enumerations, negative undecidable enumerations and all computable enumerations of a family of r.e. sets. These theorems permit to (...) strengthen the results of Pour-El, Pour-El and Howard, Ershov and Khutoretskii about existence of enumerations without repetitions and positive undecidable enumerations. (shrink)

We present several examples of hereditary classes of finite structures satisfying the joint embedding property and the weak amalgamation property, but failing the cofinal amalgamation property. These include a continuum‐sized family of classes of finite undirected graphs, as well as an example due to Pouzet with countably categorical generic limit.

The flipped classroom is becoming a popular new instructional model in higher education capable of increasing student performance in higher-order learning outcomes. However, the success of a flipped classroom model depends on various supporting elements, and it may not be appropriate for all students and courses. In this study, a new blended Biochemistry classroom model based on Massive Open Online Courses and a “semi-flipped” environment was applied to Biochemistry instruction of Nursing and Clinical Medicine majors. The students’ academic performance and (...) perceptions of self-cognition were used to assess the blended Biochemistry classroom. Students who participated in the blended classroom model achieved higher academic performance and reported a significant improvement in their perceptions of self-cognition compared to the control group. Moreover, the effectiveness of the blended Biochemistry classroom on the small size class was stronger than on the large size class. (shrink)

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and (...) PAC reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: [email protected]: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

The usual objections to infinite numbers, and classes, and series, and the notion that the infinite as such is self-contradictory, may... be dismissed as groundless. There remains, however, a very grave difficulty, connected with the contradiction [of the class of all classes not members of themselves]. This difficulty does not concern the infinite as such, but only certain very large infinite classes.

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. Motivated by results of Bagaria, Magidor and Väänänen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifically, we aim to characterize notions from the lower end of the large cardinal hierarchy through the principle [math] introduced by Bagaria and Väänänen. Our results isolate a narrow interval in the large cardinal hierarchy that is bounded from below by total indescribability and from above by subtleness, (...) and contains all large cardinals that can be characterized through the validity of the principle [math] for all classes of structures defined by formulas in a fixed level of the Lévy hierarchy. Moreover, it turns out that no property that can be characterized through this principle can provably imply strong inaccessibility. The proofs of these results rely heavily on the notion of shrewd cardinals, introduced by Rathjen in a proof-theoretic context, and embedding characterizations of these cardinals that resembles Magidor’s classical characterization of supercompactness. In addition, we show that several important weak large cardinal properties, like weak inaccessibility, weak Mahloness or weak [math]-indescribability, can be canonically characterized through localized versions of the principle [math]. Finally, the techniques developed in the proofs of these characterizations also allow us to show that Hamkin’s weakly compact embedding property is equivalent to Lévy’s notion of weak [math]-indescribability. (shrink)

We study classes of atomic models \ of a countable, complete first-order theory T. We prove that if \ is not \-small, i.e., there is an atomic model N that realizes uncountably many types over \\) for some finite \ from N, then there are \ non-isomorphic atomic models of T, each of size \.

The study of biomechanics most often takes a classic adaptationist approach, examining the functional abilities of organisms in relation to what is allowed by physical parameters. This approach generally assumes strong selection and is less concerned with evolutionary stochasticity in determining the presence of biological traits. It is equally important, however, to consider the importance of constraint in determining the form of organisms. If selection is relatively weak compared to stochastic events, then the observed forms in living systems can be (...) taken not as those shapes that were strongly selected for, so much as those forms that do not violate physical rules and therefore persist. Using the problem of maximum animal size as a case study for this alternative biomechanical philosophy, I demonstrate one example of how biomechanical approaches can be used to study constraint and consider the concept of absent forms. This alternative mindset and approach produces a complementary system to the traditional form and function approach in biomechanics. The two philosophies can be used in conjunction to better understand biological systems. I focus particularly on the maximum size of flying animals, as they are a heavily constrained class of system that has also been shaped by substantial stochasticity. (shrink)

A child’s age in comparison to the age of her or his classmates (relative age) has been found to be an influential factor on academic achievement, particularly but not exclusively at the beginning of formal schooling. However, few studies have focused on the generalizability of relative age effects. To close this gap, the present study analyzes the generalizability across students with and without immigrant backgrounds, across three student cohorts that entered school under a changing law of school enrollment, and across (...) classes. To this end, we capitalized on representative large-scale data sets from three student cohorts attending public schools in Berlin, the capital of Germany. We analyzed the data using a multilevel framework. Our results for the overall student sample indicate relative age effects for reading and mathematics in favor of the relatively older students in Grade 2 that become somewhat smaller in size in Grade 3. By Grade 8, relative age effects had vanished in reading and had even reversed in favor of the relatively young in mathematics. Furthermore, relative age effects were not found to be systematically different among students with and without immigrant backgrounds, student cohorts, or across classes. Taken together, these results empirically underscore the broad generalizability of the findings as found for the overall student population and replicate the pattern of findings on relative effects as identified by the majority of previous studies. (shrink)

As in other countries, the public in Argentina became aware of the existence of something called “the theory of relativity” only after November 1919. Although the news of Arthur Eddington's eclipse expedition, which provided the first confirmation of Einstein's theory, was poorly reported in the newspapers, by the end of 1920 Einstein had become a household name for the educated middle class of Buenos Aires, the capital city of the country. This was in great measure the result of the (...) activity of a few enthusiastic lecturers. Significantly, none of them belonged to the prestigious Institute of Physics of the University of La Plata, which during the decade of the 1910s was considered the most important center of physical research in Latin America. Between July and August 1920 the Spanish physicist Blas Cabrera – perhaps the greatest popularizer of Einstein's theory in Spain – visited Argentina and talked about relativity. In September Georges Duclout, a French engineer who had graduated from the Zurich Polytechnic and by then was professor of applied mechanics at the School of Exact, Physical and Natural Sciences of the University of Buenos Aires, also gave a series of conferences on the subject. That same month José Ubach, a Jesuit astronomer trained at the Ebro Observatory in Spain, and established in Buenos Aires, lectured on relativity at the Colegio del Salvador. (shrink)

This article has deconstructed the general phenomenon of gentrification in the historic centre of A Coruña in two models. On the one hand, a model based on social class promotion, symbolic capital and economic status in the Cidade Vella. On the other hand, the neighbourhood of Orzán as a transformation process resulting from a phenomenon of commercial gentrification based on two interrelated processes: first, the demand for new places of consumption and entertainment and second, the material devaluation of the (...) neighbourhood. In this regard, this work brings a new dimension to the global debate around commercial gentrification. (shrink)

Exact solutions of epidemic models are critical for identifying the severity and mitigation possibility for epidemics. However, solving complex models can be difficult when interfering conditions from the real-world are incorporated into the models. In this paper, we focus on the generally unsolvable adaptive susceptible-infected-susceptible epidemic model, a typical example of a class of epidemic models that characterize the complex interplays between the virus spread and network structural evolution. We propose two methods based on mean-field approximation, i.e., the first-order (...) mean-field approximation and higher-order mean-field approximation, to derive the exact solutions to ASIS models. Both methods demonstrate the capability of accurately approximating the metastable-state statistics of the model, such as the infection fraction and network density, with low computational cost. These methods are potentially powerful tools in understanding, mitigating, and controlling disease outbreaks and infodemics. (shrink)

We propose certain clases that seem unable to form a completed totality though they are very small, finite, in fact. We suggest that the existence of such clases lends support to an interpretation of the existence of proper clases in terms of availability, not size.

This investigation places recent research about changes in wives' and husbands' domestic labor in the context of well-known reporting differences between different kinds of housework surveys. An analysis of the “reporting gap” between direct-question reports of housework hours from the National Survey of Families and Households and time-diary reports from Americans' Use of Time, 1985, shows that both husbands and wives overreport their housework contributions. Furthermore, gender attitudes, total housework, class, education, income, family size, and employment status together (...) significantly affect the overreport, although the variables operate in different ways for wives and husbands. It is concluded that changing and uneven social perceptions of the appropriate domestic roles of women and men have resulted in reporting biases that do not necessarily correspond to actual changes in housework behavior. These findings cast doubt on claims that contemporary husbands are doing more housework than their predecessors. (shrink)

We report two studies on the effect of implicitly versus explicitly conveying affirmation and denial problems about conditionals. Recently Evans and Handley (1999) and Schroyens et al. (1999b, 2000b) showed that implicit referencing elicits matching bias: Fewer determinate inferences are made, when the categorical premise (e.g., B) mismatches the conditional's referred clause (e.g., A). Also, the effect of implicit affirmation (B affirms not-A) is larger than the effect of implicit denial (B denies A). Schroyens et al. hypothesised that this interaction (...) is due to uncertainty in the case-wise affirmation of the contrast class of negated elements involved in implicit affirmations. In Experiment 1 we tested this hypothesis by manipulating the set size of the conditional clauses. The results confirm that binary sets, where the contrast class is a singleton, eliminate the differential effect of implicit affirmation and denial. With non-binary sets the interaction is not modulated by the scope of the contrast class (3, 5, 9 elements). Experiment 2 further investigated the role of contrast classes by using class inclusion to construct implicit affirmations (Mammal vs Mammal or Monkey) and implicit denial (No-Mammal vs Mammal or Monkey), in addition to the standard implicit problems mediated by contrast-class inclusion [(No-)Mammal/No-Mammal; Reptile; Snake). Findings indicate that class inclusion (Mammal/Monkey; Reptile/ Snake) only marginally affects performance, and is independent of the type of problem. This would suggest that the implicitness problem-type interaction is dependent on constructing contrast classes. However, the experiment failed to replicate the interaction, even on the subset of problems repeating the abstract letter/number format of Experiment 1. Moreover, with the natural binary set-sizes (vowels/consonants) the implicitness effect was eliminated entirely. (shrink)

The nature of the census figures produced by Demetrius of Phaleron, crucial evidence for the size of the Athenian population, has been misunderstood. The census categories were not 'native Athenians, foreign residents and slaves', but 'citizens above the property qualification, residents without political rights and members of households'. The property qualification of 1,000 drachmas associated with Demetrius' regime was the requirement for holding the highest offices; the property requirement for citizenship rights was lower, as it was in the spurious (...) constitution of Draco described in Athenaion Politeia 4, which was probably invented and inserted during Demetrius' reign. In the light of this reinterpretation of the evidence for the structure of the Athenian population under Demetrius, a reconsideration of the evidence for the size of the Athenian population in 322 BC suggests that there were ea. 30,000 adult male citizens and far fewer metics than generally assumed, probably ea. 5,000. The distribution of property among the citizen population was very uneven, with the richest 30% of the population owning about 80% of the wealth. According to Demetrius' census as reinterpreted here, slaves outnumbered free residents by 'only' about 3:1, which still seems an implausibly high figure, but needs to be taken seriously as a government estimate rather than a rhetorical exaggeration. (shrink)

We show how to build prime models in classes of saturated models of abstract elementary classes (AECs) having a well‐behaved independence relation: Let be an almost fully good AEC that is categorical in and has the ‐existence property for domination triples. For any, the class of Galois saturated models of of size λ has prime models over every set of the form. This generalizes an argument of Shelah, who proved the result when λ is a successor cardinal.

The purpose of this study is to explore the impact of constraining class-specific residual variances to be equal by examining and comparing the parameter estimation of a free model and a constrained model under various conditions. A Monte Carlo simulation study was conducted under several conditions, including the number of predictors, class-specific intercepts, sample size, class-specific regression weights, and class proportion to evaluate the results for parameter estimation of the free model and the restricted model. (...) The free model yielded a more accurate estimation than the restricted model for most of the conditions, but the accuracy of the free model estimation was impacted by the number of predictors, sample size, the disparity in the magnitude of class-specific slopes and intercepts, and class proportion. When equality constraints were imposed in residual variance discrepant conditions, the parameter estimates showed substantial inaccuracy for slopes, intercepts, and residual variances, especially for those in Class 2. When the residual variances were equal between the classes, the restricted model showed better performance under some conditions. (shrink)

We improve results of Marczewski, Frankiewicz, Brown, and others comparing the σ-ideals of measure zero, meager, Marczewski measure zero, and completely Ramsey null sets; in particular, we remove CH from the hypothesis of many of Brown's constructions of sets lying in some of these ideals but not in others. We improve upon work of Marczewski by constructing, without CH, a nonmeasurable Marczewski measure zero set lacking the property of Baire. We extend our analysis of σ-ideals to include the completely Ramsey (...) null sets relative to a Ramsey ultrafilter and obtain all 32 possible examples of sets in some ideals and not others, some under the assumption of MA, but most in ZFC alone. We also improve upon the known constructions of a Marczewski measure zero set which is not Ramsey by using a set theoretic hypothesis which is weaker than those used by other authors. We give several consistency proofs: one concerning the relative sizes of the covering numbers for the meager sets and the completely Ramsey null sets; another concerning the size of non(CRU 0); and a third concerning the size of add(CRU 0). We also study those classes of perfect sets which are bases for the class of always first category sets. (shrink)

We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at singular cardinals satisfying mild set-theoretic hypotheses. This had previously been (...) open even for the random graph. We characterize supersimplicity of countable theories in terms of having PC-exact saturation at singular cardinals of countable cofinality. We also consider the local analog of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Great World House: Martin Luther King Jr. and Global Ethics by Hak Joon Lee, and: Democracy in Twenty-First Century America: Race, Class, Religion, and Region by Ronald B. NealReggie L. WilliamsThe Great World House: Martin Luther King Jr. and Global Ethics HAK JOON LEE Cleveland, OH: Pilgrim Press, 2011. 256 pp. $25.00Democracy in Twenty-First Century America: Race, Class, Religion, and Region RONALD B. NEAL Macon, (...) GA: Mercer University Press, 2012. 138 pp. $30.00On Christmas Eve 1967, Martin Luther King Jr. asked the members of a congregation to recognize that they are—every day—interacting with many different nations all around the world as they maneuver throughout their normal daily routines. Hak Joon Lee’s The Great World House: Martin Luther King Jr. and Global Ethics examines the implications of this daily global interaction as the need for a broader ethical perspective in a shrinking world. The need begins with the realization that we do indeed inhabit a shrinking world in which our local behavior has a broader global impact. Once we recognize the moral implications of our local interaction, it becomes clear that we must learn how to live together in a broader community.But how do we speak the language of a global morality? What does a global morality look like? Lee argues that King’s metaphor of a great world house provides a structure on which to frame the content of a healthy global morality in a shrinking world. The metaphor indicates a collective understanding of all humanity as a global community (ix). The notion of a single world house moves people groups beyond rival communities with well-defined in-group and out-group barriers into what Lee describes as a global civil society where we are all seen as members of a collective in-group (13). The concept of a collective in-group helps illustrate what Lee understands to be King’s argument for a global morality; “King’s idea of a great world house redefines what the boundaries and membership of a moral community are: the great world house constitutes a single inclusive ethical community for humanity because it identifies the world as a single unified community” (53). [End Page 234]But as laudable as King’s great world house metaphor is, we are still burdened with the task of imagining a universal moral language in practice. Efforts toward the formation of universal truths have historically been death-dealing for people groups caught on the wrong side of the color line. A one-size-fits-all morality has been a procrustean bed for people who have been racialized and subordinated to white European males. Yet Lee interprets King’s method of universal engagement to begin with convictions shared at home within the particularity of his African American Christian worldview before it moves outward toward a shared vision of a global civil society. The movement from particular to universal for a public morality is unlike the historically harmful practice of universal morality. King’s universal method includes attention to four components: vision, norms, virtues, and political practices. These four components belong to what Lee depicts as a careful and intricate dialectic between what is local and what is universal in a political dialogue that seeks the end of a global civil society with shared conceptions of community and human rights.Ironically, with regard to the conversation about human rights, Lee claims that King’s formative African American interpretation of human rights was primarily informed by the Enlightenment and then blended with an African American experience: “Mostly appropriated from Christianity and the Western Enlightenment tradition, these norms [justice, freedom, and equality] obtained a new significance for African Americans in the context of the sizzling cauldron of slavery and segregation” (55). Yet one would be hard pressed to identify the presence of modern Enlightenment intellectuals within the formative theological worldview of the African American Christianity that Lee identifies. Of necessity, African American Christianity, the Christian worldview that birthed Martin Luther King Jr., was formed to deflect the white Christian worldview that was shaped by the intersection of race, religion, and empire in modernity. The Enlightenment fueled modernity’s... (shrink)

The Feferman–Vaught theorem provides a way of evaluating a first order sentence \(\varphi \) on a disjoint union of structures by producing a decomposition of \(\varphi \) into sentences which can be evaluated on the individual structures and the results of these evaluations combined using a propositional formula. This decomposition can in general be non-elementarily larger than \(\varphi \). We introduce a “tree” generalization of the prenex normal form (PNF) for first order sentences, and show that for an input sentence (...) in this form having a fixed number of quantifier alternations, a Feferman–Vaught decomposition can be obtained in time elementary in the size of the sentence. The sentences in the decomposition are also in tree PNF, and further have the same number of quantifier alternations and the same quantifier rank as the input sentence. We extend this result by considering binary operations other than disjoint union, in particular sum-like operations such as join, ordered sum and NLC-sum, that are definable using quantifier-free translation schemes. (shrink)

During spring of 2020, environmental ethics students at a medium sized metropolitan university in the Southeastern United States were asked to read and comment on classic essays from Robert Heilbroner and Garrett Hardin, essays regarding our responsibilities towards future generations. In general, students seemed to hold more with Heilbroner’s stance, which left room for compassion, while condemning Hardin’s harshness. Students were then asked to provide written responses stating whether they would personally sacrifice their eventual retirement in order to stop COVID-19 (...) and the reasons for their views. Responses were analyzed and categorized to detect inconsistencies between students’ described views and their willingness to personally sacrifice for the sake of others. Almost 72% of respondents asserted that they would be willing to intervene to stop the novel coronavirus by sacrificing their retirement. A fair number of respondents that stated they would sacrifice said that they would do so because they would benefit personally from the avoidance of guilt and/or from the opportunity to feel good about themselves, suggesting that even seemingly selfless behaviors are sometimes driven by egoistic motivations. Forty percent of all respondents held inconsistent views. Most notably, a number of students condemned Hardin for his lack of compassion, yet were not willing to act compassionately themselves. (shrink)

The Islamization of the Malaysian media industry has created a debate on whether Islam has been truly adopted for its religious significance or simply manipulated for commercial gains. While Islamic content is abundant, it seems to grow in size but not in value. This paper offers a political-economic look into this problem by 1) contextualizing the Islamization process in relations to Malaysia’s socio-political environment, 2) delineating the development of Islamic media in Malaysia and, 3) identifying the influence of media (...) ownership on the Islamization process by locating the role of Islam in contemporary Malaysian media. (shrink)

Working in constructive set theory we formulate notions of constructive topological space and set-generated locale so as to get a good constructive general version of the classical Galois adjunction between topological spaces and locales. Our notion of constructive topological space allows for the space to have a class of points that need not be a set. Also our notion of locale allows the locale to have a class of elements that need not be a set. Class sized (...) mathematical structures need to be allowed for in constructive set theory because the powerset axiom and the full separation scheme are necessarily missing from constructive set theory. We also consider the notion of a formal topology, usually treated in Intuitionistic type theory, and show that the category of set-generated locales is equivalent to the category of formal topologies. We exploit ideas of Palmgren and Curi to obtain versions of their results about when the class of formal points of a set-presentable formal topology form a set. (shrink)