In this article we show that it is possible to completely classify the degrees of r.e. bases of r.e. vector spaces in terms of weak truth table degrees. The ideas extend to classify the degrees of complements and splittings. Several ramifications of the classification are discussed, together with an analysis of the structure of the degrees of pairs of r.e. summands of r.e. spaces.

We show that the Q-degree of a hyperhypersimple set includes an infinite collection of Q1-degrees linearly ordered under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\leq_{Q_1}}$$\end{document} with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q1-degrees are not an upper semilattice. The main result of this paper is that the Q1-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for \documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^0}$$\end{document}s1-degrees. (shrink)

De invloed van het denken van Paul Moyaert is zeer groot. Daarom wil 'Orde scheppen' hulde brengen aan deze filosoof en zijn intellectuele bezetenheid. De thematische diversiteit van het boek weerspiegelt de biodiversiteit van Moyaerts eigen werk, die met enig geweld tot drie grote thema's of domeinen kan worden herleid: wijsgerige antropologie, psychopathologie en religie. Onderwerpen zijn: het symbolische, de liefde, uchronie, de echtheid van beelden, en poëzie; de afstemming bij jongvolwassenen met een meervoudige handicap, homoseksualiteit bij vrouwelijke adolescenten, (...) en Kant en Foucault; en ten slotte de hardnekkigheid van religie, christelijke ascese, de vele gezichten van Kierkegaard, Franciscus van Assisi, en de oorlogsdagboeken van Hans Keilson. (shrink)

We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

We show that for every computably enumerable degree a > 0 there is an intrinsically c.e. relation on the domain of a computable structure of computable dimension 2 whose degree spectrum is { 0 , a } , thus answering a question of Goncharov and Khoussainov 55–57). We also show that this theorem remains true with α -c.e. in place of c.e. for any α∈ω∪{ω} . A modification of the proof of this result similar to what was done (...) in Hirschfeldt shows that for any α∈ω∪{ω} and any α -c.e. degrees a 0 ,…, a n there is an intrinsically α -c.e. relation on the domain of a computable structure of computable dimension n+1 whose degree spectrum is { a 0 ,…, a n } . These results also hold for m-degree spectra of relations. (shrink)

This book presents new results in computability theory, a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field's connections with disparate areas of mathematical logic and mathematics more generally have grown deeper, and now have a variety of applications in topology, group theory, and other subfields. This monograph establishes new directions in the field, blending classic results with modern research areas such as algorithmic randomness. The significance of the book lies not only (...) in the depth of the results contained therein, but also in the fact that the notions the authors introduce allow them to unify results from several subfields of computability theory. (shrink)

I argue here that the impairment principle requires clarification. It needs to explain what makes one impairment greater than another, otherwise we will be unable to make the comparisons it requires, the ones that enable us to determine whether b really is a greater impairment than a, and as a result, whether causing b is immoral because causing a is. I then develop two of what I think are the most natural accounts of what might make one impairment greater than (...) another. The quantitative understanding of greater impairment is problematic because it leaves the impairment principle vulnerable to counterexamples; just because impairment b impairs a larger number of abilities or the same number of abilities but for a longer period or to a higher degree does not mean that b is a greater impairment than a. The qualitative understanding of greater impairment is problematic because it does not explain examples of greater impairment used in the literature, means that an abortion is always a qualitatively more severe impairment than causing fetal alcohol syndrome regardless of how the organism is affected, and/or entails that lethal impairment is always greater than nonlethal impairment. (shrink)

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given (...) class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings ; integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. This allows us to show that several theorems about degree spectra of relations on computable structures, nonpreservation of computable categoricity, and degree spectra of structures remain true when we restrict our attention to structures in any of the classes on this list. The codings we present are general enough to be viewed as establishing that the theories mentioned above are computably complete in the sense that, for a wide range of computability-theoretic nonstructure type properties, if there are any examples of structures with such properties then there are such examples that are models of each of these theories. (shrink)

Teaching for social justice requires an ability to address sensitive issues such as racism and sexism so that students can gain critical consciousness of these pervasive social realities. However, the empirical literature thus far provides minimal exploration of the factors teachers consider in deciding how to address these issues. This study explores this question through ethnographic case studies of two urban, 11th grade U.S. History classrooms. Differing classroom racial demographics and teacher instructional goals resulted in two distinct pedagogical approaches to (...) social justice teaching. Despite differences in class makeup and teaching approach, students in both classrooms developed intellectual confidence and critical citizenship skills related to their growing sociopolitical awareness. (shrink)

We study the weak truth table degree spectra of first-order relational structures. We prove a dichotomy among the possible wtt degree spectra along the lines of Knight’s upward-closure theorem for Turing degree spectra. We prove new results contrasting the wtt degree spectra of finite- and infinite-signature structures. We show that, as a method of defining classes of reals, the wtt degree spectrum is, except for some trivial cases, strictly more expressive than the Turing degree (...) spectrum. (shrink)

ABSTRACT R. P. Wolff has argued that there is an irreconcilable conflict between the distinguishing mark of every state, viz. supreme authority over all its citizens, and the primary obligation of rational beings, viz. to act autonomously by taking moral responsibility for all of their actions. Utilitarian and consent theories which seek to justify the state's claim to possess a monopoly of the rightful use of force are shown to fail and the concept of a ‘legitimate state’to be morally incoherent. (...) However, Wolff's version of individualist anarchism does not follow. Human beings are by no means equally rational or homogeneously autonomous. There are ‘states’which have a contingent and variable right to enforce obedience over an indefinitely large number of their ‘subjects’, although not over those who are autonomous because rational in high degree. (shrink)

Informal construction -- Formal construction -- Limiting results.

Background and aim With the increasing interest in lifestyle, health and consequences of unhealthy lifestyles for the healthcare system, a new kind of solidarity is gaining importance: lifestyle solidarity. While it might not seem fair to let other people pay for the costs arising from an unhealthy lifestyle, it does not seem fair either to punish people for their lifestyle. However, it is not clear how solidarity is assessed by people, when considering disease risks or lifestyle risks. The aim of (...) this study was to investigate the degree of solidarity with lifestyle as well as with other factors that are related to health outcomes—for example, old age—and the relation between this degree of solidarity and various characteristics. Methods This cross-sectional study is part of the Dutch longitudinal SMILE study. Data on the degree of solidarity with different lifestyles and old age, and the relation between the degree of solidarity and various demographic and other variables were obtained in a questionnaire survey. Results Solidarity with smokers and overweight people was moderate, as was solidarity with older people. Respondents were ambivalent about athletes. Respondents who were younger, male and highly educated, and those with a healthy lifestyle, a small social network, high quality of life and an internal locus of control, showed low solidarity. Conclusions Solidarity with an unhealthy lifestyle and old age is moderate and the degree of solidarity varies among the different subgroups. (shrink)

We say that A≤LRB if every B-random set is A-random with respect to Martin–Löf randomness. We study this relation and its interactions with Turing reducibility, classes, hyperimmunity and other recursion theoretic notions.

We consider the set of jumps below a Turing degree, given by JB={x':x≤a}, with a focus on the problem: Which recursively enumerable degrees a are uniquely determined by JB? Initially, this is motivated as a strategy to solve the rigidity problem for the partial order R of r.e. degrees. Namely, we show that if every high2 r.e. degree a is determined by JB, then R cannot have a nontrivial automorphism. We then defeat the strategy—at least in the form (...) presented—by constructing pairs a0, a1 of distinct r.e. degrees such that JB=JB within any possible jump class {x:x'=c}. We give some extensions of the construction and suggest ways to salvage the attack on rigidity. (shrink)

There has been increasing interest over the last few decades in the study of the effective content of Mathematics. One field whose effective content has been the subject of a large body of work, dating back at least to the early 1960s, is model theory. Several different notions of effectiveness of model-theoretic structures have been investigated. This communication is concerned withcomputablestructures, that is, structures with computable domains whose constants, functions, and relations are uniformly computable.In model theory, we identify isomorphic structures. (...) From the point of view of computable model theory, however, two isomorphic structures might be very different. For example, under the standard ordering of ω the success or relation is computable, but it is not hard to construct a computable linear ordering of type ω in which the successor relation is not computable. In fact, for every computably enumerable degree a, we can construct a computable linear ordering of type ω in which the successor relation has degree a. It is also possible to build two isomorphic computable groups, only one of which has a computable center, or two isomorphic Boolean algebras, only one of which has a computable set of atoms. Thus, for the purposes of computable model theory, studying structures up to isomorphism is not enough. (shrink)

When used in conjunction with the current floorplan and the optimization technique in circuit design engineering, this research allows for the evaluation of design parameters that can be used to reduce congestion during integrated circuit fabrication. Testing the multiple alternative consequences of IC design will be extremely beneficial in this situation, as will be demonstrated further below. If the importance of placement and routing congestion concerns is underappreciated, the IC implementation may experience significant nonlinear problems throughout the process as a (...) result of the underappreciation of placement and routing congestion concerns. The use of standard optimization techniques in integrated circuit design is not the most effective strategy when it comes to precisely estimating nonlinear aspects in the design of integrated circuits. To this end, advanced tools such as Xilinx VIVADO and the ICC2 have been developed, in addition to the ICC1 and VIRTUOSO, to explore for computations and recover the actual parameters that are required to design optimal placement and routing for well-organized and ordered physical design. Furthermore, this work employs the perimeter degree technique to measure routing congestion in both horizontal and vertical directions for a silicon chip region and then applies the technique to lower the density of superfluous routing. Recently, a metaheuristic approach to computation has increased in favor, particularly in the last two decades. It is a classic graph theory problem, and it is also a common topic in the field of optimization. However, it does not provide correct information about where and how nodes should be put, despite its popularity. Consequently, in conjunction with the optimized floorplan data, the optimized model created by the Improved Harmonic Search Optimization algorithm undergoes testing and investigation in order to estimate the amount of congestion that occurs during the routing process in VLSI circuit design and to minimize the amount of congestion that occurs. (shrink)

The Bell–Kochen–Specker theorem shows that, in any Hilbert space of dimension of at least 3, it is impossible to assign noncontextual definite values to all observables in such a way that the quantum-mechanical predictions are reproduced. This leaves open the issue of what subsets of observables may be assigned definite values. Clifton has shown that, for a system of at least two continuous degrees of freedom, it is not possible to assign simultaneous noncontextual values to two coordinates and their conjugate (...) momenta. In this Letter, it is shown that, for a system of a single continuous degree of freedom, it is not possible to assign noncontextual values to the coordinate and its conjugate momenta that satisfy a continuity assumption herein called the ‘ -Product Rule’.  2002 Elsevier Science B.V. All rights reserved. (shrink)

The "Kinsey Report" suggests the existence of such a mentality. Of 142 women with much homosexual experience, 70 percent reported no regrets. This consciousness has manifested itself in literature in two ways. First, in lesbian romanticism: fusions of life and death, happiness and woe, natural imagery and supernatural strivings, neoclassical paganism with a ritualistic cult of Sappho, and modern beliefs in evolutionary progress with a cult of the rebel. At its worst an inadvertent parody of fin de siecle decadence, at (...) its best lesbian romanticism ruthlessly rejects a stifling dominant culture and asserts the value of psychological autonomy, women, art, and a European civilization of the sensuous, sensual, and voluptuous. Woolf's Orlando is its most elegant and inventive text, but its symbol is probably the career of Natalie Barney, the cosmopolitan American who was the prototype of Valerie Seymour.23· 23. See Rubin, introduction to Vivien's A Woman Appeared to Me, and George Wickes, The Amazon of Letters: The Life and Loves of Natalie Barney .Catherine R. Stimpson, professor of English at Rutgers University, is the former editor of Signs: Journal of Women in Culture and Society. The author of both critical essays and fiction, she recently co-edited, with Ethel Spector Person, Women, Sex and Sexuality. (shrink)

The theoretical framework adopted in the exact sciences, for constructing and testing deterministic theories on the one hand, and modelling and analysis of observed phenomena on the other, is often implicitly assumed to be that of structural stability. In view of recent developments in nonlinear dynamics, it is argued here that in general it may not be possible to assume strict determinism and structural stability simultaneously; either strict determinism holds, in which case the fragility framework may turn out to be (...) the appropriate framework for the study of certain phenomena in the exact sciences, or ‘structural stability’ is restored at the expense of introducing stochasticity. In this sense a certain degree of indeterminacy may be unavoidable even at the classical level. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:CHRISTOLOGY IN POLITICAL AND LIBERATION THEOLOGY R. R. RENO Creighton University Omaha, Nebraska Then I saw heaven opened, and behold, a white horse! He who sat upon it is called Faithful and True, and in righteousness he judges and makes war. His eyes are like a flame of fire, and on his head are many diadems ; and he has a name inscribed which no one knows but himself. (...) He is clad in a robe dipped in blood, and the name by which he is called is The Word of God. And armies of heaven, arrayed in fine linen, white and pure, followed him on white horses. From his mouth issues a sharp sword with which to smite the nations, and he will rule them with a rod of iron; he will tread the wine press of the fury of the wrath of God the Almighty. On his robe and on his thigh he has a name inscribed, King of kings and Lord of lords. Revelation 19:11-16 SHARP IS THE SWORD of The Word of God: so proclaims a growing body of literature in political and liberation theology. Although this literature evidences a deep pluralism when describing wherein the sword is sharp and toward what it is aimed, the unifying claim is that Christianity has decisive political significance. And this significance takes an explicitly theoretical form. Unlike other politically directed theological programs (e.g., Reinhold Niebuhr, Walter Rauschenbush, Paul Lehmann), political and liberation theologies do not restrict the practical to a pre- or post-theoretical moment. The practical questions of liberation and justice are internal to explicitly theological reflection. The manner in which questions of liberation and justice are 291 292 R. R. RENO woven into the fabric of theology is manifold. Juan Luis Segundo, in Liberation of Theology, presents an account of theological method which is necessarily political.1 He attempts to show that, to the degree that it is faithful, theological reflection must be constituted by ideological critique and transformative social commitment. In a similar although more ambiguous way, Matthew Lamb's Solidarity with Victims seeks to build social and political issues into the ground floor of method.2 On a different front, Jiirgen Moltmann's Theology of Hope emphasizes the necessarily political dimension of eschatology.3 Quite far removed from the radicalism of most political and liberation theologies, but equally important and increasingly self-conscious of its theological context, the Roman Catholic human rights tradition can be seen as a political theology which chooses to operate within the context of a strong doctrine of creation.4 1 Juan Luis Segundo, Liberation of Theology. (Maryknoll, New York: Orbis Books, 1976). 2 Lamb's program is more than a methodological proposal for theology in itself. He promotes an interesting mixture of critical theory and interdisciplinary study as a path for all inquiry. The result is a pastiche of Adorno and Lonergan. Lamb explains his interdiscipinary vision as follows : " Such a noetic praxis of theologizing would develop academically institutionalized ways of promoting an intellectual conversion (metanoia) whereby the suffering witness of the victims of history would challenge the systems and theories constitutive of our world experience " (Victims, p. 17). However, the critical element of this interdisciplinary "noetic praxis" which Lamb draws from Adorno's Negative Dialectics militates against this " institutionalized" use. At the deepest level Adorno questions the very possibility of a noetic practice which mediates the reality of experience, and he certainly rejects any institutional reification of the small insights which we might garner. For Adorno, critical thought cannot mediate the actual suffering of concrete individuals ; rather, its ultimate impotence in the face of such a reality mirrors the suffering of finite beings. Thought bears witness formally not materially. This basic feature of Adorno's thought runs counter to Lonergan's cognitive optimism, making Lamb's program interesting but implausible. Matthew Lamb, Solidarity with Victims (New York: Crossroad, 1982). SJiirgen Moltmann, Theology of Hope. (New York: Harper & Row, 1967). 4 David Hollenbach's Claims in Confiict (New York: Paulist Press, 1979) provides an example of a recent attempt to uncover the theological foundations for a theory of rights. Showing that the language of rights flows from a basic respect... (shrink)