Jullien's indecomposability theorem (INDEC) states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis, and then, in the base system RCA₀ plus ${\mathrm{\Sigma }}_{1}^{1}\text{\hspace{0.17em}}$ induction, it was shown by Neeman to have strength strictly between weak ${\mathrm{\Sigma }}_{1}^{1}$ choice and ${\mathrm{\Delta }}_{1}^{1}$ comprehension. We prove in this paper that ${\mathrm{\Sigma }}_{1}^{1}$ induction is needed (...) for the reversal of INDEC, that is for the proof that INDEC implies weak ${\mathrm{\Sigma }}_{1}^{1}$ choice. This is in contrast with the typical situation in reverse mathematics, where reversals can usually be refined to use only ${\mathrm{\Sigma }}_{1}^{0}$ induction. (shrink)

In this paper I shall present a method for proving determinacy from large cardinals which, in many cases, seems to yield optimal results. One of the main applications extends theorems of Martin, Steel and Woodin about determinacy within the projective hierarchy. The method can also be used to give a new proof of Woodin's theorem about determinacy in L.The reason we look for optimal determinacy proofs is not only vanity. Such proofs serve to tighten the connection between large cardinals and (...) descriptive set theory, letting us bring our knowledge of one subject to bear on the other, and thus increasing our understanding of both. A classic example of this is the Harrington-Martin proof that -determinacy implies -determinacy. This is an example of a transfer theorem, which assumes a certain determinacy hypothesis and proves a stronger one. While the statement of the theorem makes no mention of large cardinals, its proof goes through 0#, first proving that-determinacy ⇒ 0# exists,and then that0# exists ⇒ -determinacyMore recent examples of the connection between large cardinals and descriptive set theory include Steel's proof thatADL ⇒ HODL ⊨ GCH,see [9], and several results of Woodin about models of AD+, a strengthening of the axiom of determinacy AD which Woodin has introduced. These proofs not only use large cardinals, but also reveal a deep, structural connection between descriptive set theoretic notions and notions related to large cardinals. (shrink)

The dichotomy between Nature and Nurture, which has been dismantled within the framework of development, remains embodied in the notions of plasticity and evolvability. We argue that plasticity and evolvability, like development and heredity, are neither dichotomous nor distinct: the very same mechanisms may be involved in both, and the research perspective chosen depends to a large extent on the type of problem being explored and the kinds of questions being asked. Epigenetic inheritance leads to transgenerationally extended plasticity, and developmentally-induced (...) heritable epigenetic variations provide additional foci for selection that can lead to evolutionary change. Moreover, hereditary innovations may result from developmentally induced large-scale genomic repatterning events, which are akin to Goldschmidtian “systemic mutations”. The epigenetic mechanisms involved in repatterning can be activated by both environmental and genomic stress, and lead to phylogenetic as well as ontogenetic changes. Hence, the effects and the mechanisms of plasticity directly contribute to evolvability. (shrink)

We present an approach to forcing with finite sequences of models that uses models of two types. This approach builds on earlier work of Friedman and Mitchell on forcing to add clubs in cardinals larger than $\aleph_{1}$, with finite conditions. We use the two-type approach to give a new proof of the consistency of the proper forcing axiom. The new proof uses a finite support forcing, as opposed to the countable support iteration in the standard proof. The distinction is important (...) since a proof using finite supports is more amenable to generalizations to cardinals greater than $\aleph_{1}$. (shrink)

We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.

Halley et al. (2023) highlight important equity challenges emerging out of existing health policy’s reliance on self- and family advocacy. As advocacy capacity varies dramatically across groups, pu...

We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice.

Species’ adaptation to their environments occurs via a range of mechanisms of adaptation. These include genetic adaptations as well as non-traditional inheritance mechanisms such as learned behaviors, niche construction, epigenetics, horizontal gene transfer, and alteration of the composition of a host’s associated microbiome. We propose to supplement these with another modality of eco-evolutionary dynamics: cases in which adaptation to the environment occurs via what may be called a “distributed adaptation,” in which the adaptation is not conferred via something carried by (...) an individual of the adapted species (as with genes, behavior, or associated microbes), but by some structural or compositional aspect of the population. Put differently, the adaptively relevant information cannot be reduced to information possessed by a single individual, whether genetic or otherwise. Rather, the adaptively relevant information is distributed, and is found strictly at the population level. While human culture is presumably such a case, as may be cases found in social insects, we want to suggest that there are other cases that belong to this category and to explore its evolutionary implications. In particular, we discuss the factors that affect whether adaptive information is stored in a distributed way, to what degree, and what kinds of adaptive information are most likely to be found in this modality of adaptation. (shrink)

This paper applies the conceptual toolkit of Evolutionary Developmental Biology (evo‐devo) to the evolution of the genome and the role of the genome in organism development. This challenges both the Modern Evolutionary Synthesis, the dominant view in evolutionary theory for much of the 20th century, and the typically unreflective analysis of heredity by evo‐devo. First, the history of the marginalization of applying system‐thinking to the genome is described. Next, the suggested framework is presented. Finally, its application to the evolution of (...) genome modularity, the evolution of induced mutations, the junk DNA versus ENCODE debate, the role of drift in genome evolution, and the relationship between genome dynamics and symbiosis with microorganisms are briefly discussed. (shrink)

Jullien's indecomposability theorem states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis. We identify the strength of the theorem relative to standard reverse mathematics markers. We show that it lies strictly between weak [Formula: see text] choice and [Formula: see text] comprehension.

We extend the construction of Mitchell and Steel to produce iterable fine structure models which may contain Woodin limits of Woodin cardinals, and more. The precise level reached is that of a cardinal which is both a Woodin cardinal and a limit of cardinals strong past it.

A $\Sigma _{1}^{2}$ truth for λ is a pair 〈Q, ψ〉 so that Q ⊆ Hλ, ψ is a first order formula with one free variable, and there exists B ⊆ Hλ+ such that (Hλ+; ε, B) $(H_{\lambda +};\in ,B)\vDash \psi [Q]$ . A cardinal λ is $\Sigma _{1}^{2}$ indescribable just in case that for every $\Sigma _{1}^{2}$ truth 〈Q, ψ〉 for λ, there exists $\overline{\lambda}<\lambda $ so that $\overline{\lambda}$ is a cardinal and $\langle Q\cap H_{\overline{\lambda}},\psi \rangle $ is a (...) $\Sigma _{1}^{2}$ truth for $\overline{\lambda}$ . More generally, an interval of cardinals [κ, λ] with κ ≤ λ is $\Sigma _{1}^{2}$ indescribable if for every $\Sigma _{1}^{2}$ truth 〈Q, ψ〉 for λ, there exists $??\leq \overline{\lambda}<\kappa,??\subseteq H_{\overline{\lambda}}$ , and π: $H_{\overline{\lambda}}\rightarrow H_{\lambda}$ so that $??$ is a cardinal, $\langle ??,\psi \rangle $ is a $\Sigma _{1}^{2}$ truth for $??$ , and π is elementary from $(H_{\overline{\lambda}};\in,??,??)$ with $\pi \,|\,??={\rm id}$ . We prove that the restriction of the proper forcing axiom to c-linked posets requires a $\Sigma _{1}^{2}$ indescribable cardinal in L, and that the restriction of the proper forcing axiom to c⁺-linked posets, in a proper forcing extension of a fine structural model, requires a $\Sigma _{1}^{2}$ indescribable 1-gap [κ, κ⁺]. These results show that the respective forward directions obtained in " Hierarchies of Forcing Axioms I" by Neeman and Schimmerling are optimal. (shrink)

We prove (Proposition 2.1) that if $\mu$ is a generically stable measure in an NIP (no independence property) theory, and $\mu(\phi(x,b))=0$ for all $b$ , then for some $n$ , $\mu^{(n)}(\exists y(\phi(x_{1},y)\wedge \cdots \wedge\phi(x_{n},y)))=0$ . As a consequence we show (Proposition 3.2) that if $G$ is a definable group with fsg (finitely satisfiable generics) in an NIP theory, and $X$ is a definable subset of $G$ , then $X$ is generic if and only if every translate of $X$ does not (...) fork over $\emptyset$ , precisely as in stable groups, answering positively an earlier problem posed by the first two authors. (shrink)

The tree property at κ+ states that there are no Aronszajn trees on κ+, or, equivalently, that every κ+ tree has a cofinal branch. For singular strong limit cardinals κ, there is tension between the tree property at κ+ and failure of the singular cardinal hypothesis at κ; the former is typically the result of the presence of strongly compact cardinals in the background, and the latter is impossible above strongly compacts. In this paper, we reconcile the two. We prove (...) from large cardinals that the tree property at κ+ is consistent with failure of the singular cardinal hypothesis at κ. (shrink)

A first order theory T of power λ is called unidimensional if any twoλ+-saturated models of T of the same cardinality are isomorphic. We prove here that such theories are superstable, solving a problem of Shelah. The proof involves an existence theorem and a definability theorem for definable groups in stable theories, and an analysis of their relation to regular types.

We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both □ and □δ fail, then δ is subcompact in a class inner model. If in addition □ fails, we prove that δ is Π12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^2}$$\end{document} subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. As a corollary (...) we also see that assuming the existence of a Woodin cardinal δ so that SBHδ holds, the Proper Forcing Axiom implies the existence of a class inner model with a Π12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^2}$$\end{document} subcompact cardinal. Our methods generalize to higher levels of the large cardinal hierarchy, that involve long extenders, and large cardinal axioms up to δ is δ+ supercompact for all n < ω. We state some results at this level, and indicate how they are proved. (shrink)

We present two applications of forcing with finite sequences of models as side conditions, adding objects of size \. The first involves adding a \ sequence and variants of such sequences. The second involves adding partial weak specializing functions for trees of height \.

A biographical sketch of the Hologenome Theory.

We show that knowledge satisfies _interpersonal independence_, meaning that a non-trivial sentence describing one agent’s knowledge cannot be equivalent to a sentence describing another agent’s knowledge. The same property of interpersonal independence holds, mutatis mutandis, for belief. In the case of knowledge, interpersonal independence is implied by the fact that there are no non-trivial sentences that are common knowledge in every model of knowledge. In the case of belief, interpersonal independence follows from a _strong interpersonal independence_ that knowledge does not (...) have. Specifically, there is no sentence describing the beliefs of one person that implies a sentence describing the beliefs of another person. (shrink)

Organisms inherit various kinds of developmental information and cues from their parents. The study of inheritance systems is aimed at identifying and classifying the various mechanisms and processes of heredity, the types of hereditary information that is passed on by each, the functional interaction between the different systems, and the evolutionary consequences of these properties. We present the discussion of inheritance systems in the context of several debates. First, between proponents of monism about heredity (gene-centric views), holism about heredity (Developmental (...) Systems Theory), and those stressing the role of multiple systems of inheritance. Second, between those analyzing inheritance solely in terms of replication and transmission, and views that stress the multi-generation reproduction of phenotypic traits. A third debate is concerned with different criteria that have been proposed for identifying and delimiting inheritance systems. A fourth controversy revolves around the significance of the “Lamarckian” aspects of some of the inheritance systems that have been identified, such as epigenetic inheritance and behavioral inheritance, that allow the transmission of environmentally induced characters (i.e., “soft inheritance”). (shrink)

The “Encyclopedia of DNA Elements” (ENCODE) project was launched by the US National Human Genome Research Institute in the aftermath of the Human Genome Project (HGP). It aimed to systematically map the human transcriptome, and held the promise that identifying potential regulatory regions and transcription factor binding sites would help address some of the perplexing results of the HGP. Its initial results published in 2012 produced a flurry of high-impact publications as well as criticisms. Here we put the results of (...) ENCODE and the work on epigenomics that followed in a broad theoretical and historical context, focusing on three strands of research. The first is the history of thinking about the organization of genomes, both physical and regulatory. The second is the history of ideas about gene regulation, primarily in eukaryotes. Finally, and connecting these two issues, we suggest how to think about the role of genetic material in physiology and development. (shrink)

Introduction The purpose of this study is to characterize a conception of prayer that plays an important role in the religious thought of the medieval ...

A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure.

We present a characterization of supercompactness measures for ω1 in L(R), and of countable products of such measures, using inner models. We give two applications of this characterization, the first obtaining the consistency of $\delta_3^1 = \omega_2$ with $ZFC+AD^{L(R)}$ , and the second proving the uniqueness of the supercompactness measure over ${\cal P}_{\omega_1} (\lambda)$ in L(R) for $\lambda > \delta_1^2$.

Using methods of geometric stability , we determine the structure of Abelian groups definable in ACFA, the model companion of fields with an automorphism. We also give general bounds on sets definable in ACFA. We show that these tools can be used to study torsion points on Abelian varieties; among other results, we deduce a fairly general case of a conjecture of Tate and Voloch on p-adic distances of torsion points from subvarieties.

This article describes how empirical discoveries in the 1930s–1950s regarding population variation for chromosomal inversions affected Theodosius Dobzhansky and Richard Goldschmidt. A significant fraction of the empirical work I discuss was done by Dobzhansky and his coworkers; Goldschmidt was an astute interpreter, with strong and unusual commitments. I argue that both belong to a mechanistic tradition in genetics, concerned with the effects of chromosomal organization and systems on the inheritance patterns of species. Their different trajectories illustrate how scientists’ commitments affect (...) how they interpret new evidence and adjust to it. Dobzhansky was moved to revised views about selection, while Goldschmidt moved his attention to different genetic phenomena. However different, there are significant connections between the two that enrich our understanding of their views. I focus on two: the role of developmental considerations in Dobzhansky’s thought and the role of neutrality and drift in Goldschmidt’s evolutionary account. Dobzhansky’s struggle with chromosomal variation is not solely about competing schools of thought within the selectionist camp, as insightfully articulated by John Beatty, but also a story of competition between selectionist thinking and developmental perspectives. In contraposition, Goldschmidt emphasized the role of low penetrance mutations that spread neutrally and pointed out that drift could result from developmental canalization. This account adds to the dominant story about Goldschmidt’s resistance to the splitting of development from genetics, as told by Garland Allen and Michael Dietrich. The story I tell illustrates how developmental thinking and genetic thinking conflicted and influenced researchers with different convictions about the significance of chromosomal organization. (shrink)

We present two ways in which the model L(R) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing; we show further that a set of ordinals in V cannot be added to L(R) by small forcing. The large cardinal needed corresponds to the consistency strength of AD L (R); roughly ω Woodin cardinals.

Many natural and biological phenomena can be depicted as networks. Theoretical and empirical analyses of networks have become prevalent. I discuss theoretical biases involved in the delineation of biological networks. The network perspective is shown to dissolve the distinction between regulatory architecture and regulatory state, consistent with the theoretical impossibility of distinguishing a priori between “program” and “data”. The evolutionary significance of the dynamics of trans-generational and inter-organism regulatory networks is explored and implications are presented for understanding the evolution of (...) the biological categories development-heredity; plasticity-evolvability; and epigenetic-genetic. (shrink)

Recent and not so recent advances in our molecular understanding of the genome make the once prevalent view of the genome as a passive container of genetic information (i.e., genes) untenable, and emphasize the importance of the internal organization and re-organization dynamics of the genome for both development and evolution. While this conclusion is by now well accepted, the construction of a comprehensive conceptual framework for studying the genome as a dynamic system, capable of self-organization and adaptive behavior is still (...) underway. This work deals with the effect of such a conceptual shift on evolutionary thought. Specifically, I try to articulate the conceptual commitments and obligations of views that privilege explanatorily or causally the genome, its dynamics and mechanisms, over genes. I refer to this class of views as belonging to ‘the genome perspective’. (shrink)

Persistent activity can be the product of mechanisms other than attractor reverberations. The single-unit data presented by Amit cannot discriminate between the different mechanisms. In fact, single-unit data do not appear to be adequate for testing neural network models.

[1]: meha-haḳdamah ṿe-ʻad pereḳ 19 --.

Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.

Listening effort has been known to characterize speech recognition in noise regardless of hearing sensitivity and age. Whereas the behavioral measure of dual-task paradigm effectively manifests the cognitive cost that listeners exert when processing speech in background noise, there is no consensus as to a clinical procedure that might best express LE. In order to assess the cognitive load underlying speech recognition in noise and promote counselling for coping strategies, a feasible clinical paradigm is warranted. The ecological validity of such (...) a paradigm might best be demonstrated in middle-aged adults, exhibiting intact hearing sensitivity on one hand, however, experiencing difficulties in degraded listening conditions, unaware of the implicated cognitive cost of speech recognition in noise. To this end, we constructed a dual-task paradigm that consists of a primary task of sentences-in-noise recognition and a secondary task of simple visual colored-shape matching. Research objective was to develop a clinical paradigm for the assessment of LE in middle-aged adults. Participants were 17 middle-aged adults and 23 young adults. All participants had normal hearing according to age. Speech stimuli consisted of the Hebrew Matrix sentences in noise test. SRTn was obtained for 80% correct identification. Visual stimuli were colored geometric shapes. Outcome measures were obtained initially for each task separately, to establish performance ability, and then obtained simultaneously. Reaction time and accuracy in the secondary task were the defined metrics for LE. Results: LE was indicated for both groups, however, was more pronounced in the middle-aged, manifested in the visual accuracy and reaction time metrics. Both groups maintained the 80% correct recognition-in-noise in the dual-task, however, the middle-aged group necessitated a better SNR of 1.4dB than the normal hearing group. Moreover, the middle-aged group was taxed in a greater prolongation of reaction time, in order to uphold the correct recognition. Conclusion: a dual-task paradigm consisting of sentences-in-noise primary task combined with a simple secondary task successfully showed different manifestations of LE in middle-aged adults compared to young adults, thus approximating the use of such a paradigm in a clinical setting. (shrink)

Answering a question of Sakai :29–45, 2013), we show that the existence of an ω1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _1$$\end{document}-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with □ω1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\square _{\omega _1, 2}$$\end{document}. By a result of Donder, volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to (...) the incompatibility of □λ,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\square _{\lambda, 2}$$\end{document} and ↠\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \twoheadrightarrow $$\end{document} for uncountable κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}. (shrink)

This study compares the argumentative writing characteristics of students from different sociocultural backgrounds. We focused on Jewish ultra-Orthodox (Haredi) students, educated in a segregated religious school for boys (yeshiva), who are now attempting to integrate in secular higher education in Israel. To better understand the unique characteristics of this population, we reviewed 92 essays written by Haredi students, and compared them with 76 essays by public education (PE) graduates. Our analysis was based on the cognitive and sociocultural perspectives of argumentation. (...) Both bottom-up and top-down criteria were used to elicit the argumentative writing characteristics either emerging from the data or based on existing theories. Our primary findings indicate that Haredi students have distinct argumentative characteristics, including the use of more complex and dialectic arguments and unique persuasive tactics. These findings are discussed in light of previous research on yeshiva learning methods and recommendations are provided for adjusting the existing higher education curricula to suit both PE and Haredi students. (shrink)