Is it possible to explain and predict the development of living things? What is development? Articulate answers to these seemingly innocuous questions are far from straightforward. To date, no systematic, targeted effort has been made to construct a unifying theory of development. This novel work offers a unique exploration of the foundations of ontogeny by asking how the development of living things should be understood. It explores the key concepts of developmental biology, asks whether general principles of development can be (...) discovered, and examines the role of models and theories.The two editors have assembled a team of leading contributors who are representative of the scientific and philosophical community within which a diversity of thoughts are growing, and out of which a theory of development may eventually emerge. They analyse a wealth of approaches to concepts, models and theories of development, such as gene regulatory networks, accounts based on systems biology and on physics of soft matter, the different articulations of evolution and development, symbiont-induced development, as well as the widely discussed concepts of positional information and morphogenetic field, the idea of a. (shrink)

No comprehensive theory of development is available yet. Traditionally, we regard the development of animals as a sequence of changes through which an adult multicellular animal is produced, starting from a single cell which is usually a fertilized egg, through increasingly complex stages. However, many phenomena that would not qualify as developmental according to these criteria would nevertheless qualify as developmental in that they imply nontrivial (e.g., non degenerative) changes of form, and/or substantial changes in gene expression. A broad, comparative (...) approach is badly needed. In the Cnidaria, for example, even the boundary between generations is problematic. Describing their life cycle in terms of metagenesis (alternation between polyp generation and medusa generation) or in terms of metamorphosis (polyp as larva or juvenile) are matters of semantics more than biology. The life cycle of other metazoans, described in textbooks in terms of larva-to-adult metamorphosis, is hardly different from a typical metagenetic life cycle of cnidarians. This applies to holometabolous insects and to marine invertebrates like sea urchins, where most of the larval cells are discarded at metamorphosis. The uncertain temporal and spatial boundaries of individual development are also shown by the widespread lack of a strict correspondence between adult and mature. A comprehensive theory of development should start with a zero principle of “developmental inertia,” corresponding to an indeterminate local self-perpetuation of cell-level dynamics. Indeterminate growth, scale-invariance, segmentation, and regeneration provide examples of developmental dynamics close to that. (shrink)

This chapter contains sections titled: Introduction The Evolving Evolutionary Synthesis Population Genetics vs. Developmental Genetics Evo‐Devo's Central Target: The Study of Evolvability Origins? Conclusion Postscript: Counterpoint Acknowledgments References.

Contrary to the traditional claim that needs for unambiguous communication about animal and plant species are best served by a single set of names ruled by international Codes, I suggest that a more diversified system is required, especially to cope with problems emerging from aggregation of biodiversity data in large databases. Departures from Linnaean nomenclature are sometimes intentional, but there are also other, less obvious but widespread forms of not Code-compliant grey nomenclature. A first problem is due to the circumstance (...) that the Codes are intended to rule over the way names are applied to species and other taxonomic units, whereas users of taxonomy need names to be applied to specimens. For different reasons, it is often impossible to refer a specimen with certainty to a named species, and in those cases an open nomenclature is employed. Second, molecular taxonomy leads to the discovery of clusters of gene sequence diversity not necessarily equivalent to the species recognized and named by taxonomists. Those clusters are mostly indicated with informal names or formulas that challenge comparison between different publications or databases. In several instances, it is not even clear if a formula refers to an individual voucher specimen, or is a provisional species name. The use of non-Linnaean names and formulas must be revised and strengthened by fixing standard formats for the different kinds of objects or hypotheses and providing permanent association of ‘grey names’ with standardized source information such as author and year. In the context of a broad-scope revisitation of aims and scope of scientific nomenclature, it may be worth rethinking if natural objects like plant galls and lichens, although other than the ‘single-entity’ objects traditionally covered by biological classifications, may nevertheless deserve taxonomic names. (shrink)

Evolutionary developmental biology is a rapidly growing discipline whose ambition is to address questions that are of relevance to both evolutionary biology and developmental biology. This field has been increasingly progressing as a new and independent comparative science. However, we argue that evo-devo’s comparative approach is challenged by several metaphysical, methodological and socio-disciplinary issues related to the foundation of heuristic functions of model organisms and the possible criteria to be adopted for their selection. In addition, new tools have to be (...) developed to deal with newly chosen model organisms. Therefore, we present a modelling framework suitable to integrate data on individual variation into evo-devo studies on new model organisms and thus to compensate for current idealization practices deliberately suppressing variation. (shrink)

A un secolo e mezzo dalla pubblicazione dell'Origine delle specie, la nozione di omologia di Owen, che implica che due organi o due funzioni a confronto possono essere riconosciuti come “la stessa cosa” continua a dominare gli attuali approcci al problema dell’omologia. L'idea che i caratteri possano “rimanere se stessi” attraverso un numero indefinito (anche se finito) di stati alternativi che si susseguono nel corso dell'evoluzione è probabilmente basato su un'interpretazione idealistica di come gli organismi si evolvono. Se si dà (...) per scontata l'esistenza di caratteristiche del corpo che conservano la loro identità nel cambiamento, l'esistenza di omologhi può essere spiegata (i) in termini di leggi universali della forma, magari nella forma moderna dello strutturalismo di processo, o (ii) come il prodotto di discendenza comune, o (iii) in termini di cause prossime responsabili della comparsa di moduli di sviluppo conservati. Tuttavia, leggendo la storia della vita attraverso la lente dell’evoluzione, appare molto problematico descrivere un organismo come una somma di caratteri che, una volta apparsi come novità evolutive, rimangono poi come unità costruttive essenzialmente immutabili tra le quali possiamo predicare (o negare) omologia. Tutti i tratti sono meglio interpretati come incroci complessi e mutevoli di un numero indeterminato di elementi e dei processi che li modellano nel corso dell’ontogenesi e della filogenesi. Di conseguenza, appare raccomandabile un approccio fattoriale, o combinatorio, all’omologia. (shrink)

This study analyzes shells of marine gastropods of a zoological museum and the Latin epithets expressing perceptual and connotative attributes that they have received in the standard, Linnaean nomenclature. Making use of the Osgood semantic differential, we presented the subjects with digital 3-D reproductions of the shell specimens to be subjectively evaluated according to 17 pairs of attributes. The results show that, overall, the subjective evaluations given by the subjects are consistent, which suggests that an intersubjective characterization of the shells (...) as wholes according to their qualitative and morphological traits is possible and scientifically explicable. This may apply to other biological items as well. The results also show that the epithets given to the shells by taxonomists do not always reflect the perceptual evaluation of the general population, being a product of the well-known ambiguity in taxonomic categorization and naming. (shrink)

According to the evolutionary theory, biodiversity is the product of change. However, biodiversity exists also because there are rules against an uncontrolled mixing of individuals or species that would create monsters such as the mythical chimera or the hybrids between lion and tiger. Unease in front of them is not necessarily proportional to the extent of the mixing. We fear most that the consequences of the breakup of a natural boundary may become lasting and uncontrollable. Boundaries, however, work also in (...) different way. First, you should not eat another member of your species. Second, individuality should not been breached by grafting together two individuals of the same species. Third, your enemy should not cross your skin unseen, to feed on you from inside. All these rules, however, are widely breached in nature. Humans have added to this catalogue, challenging borders by a diversity of practices that do not respect the boundaries within and between the species. All these practices are the ultimate treat – material and cultural alike – to the survival of biodiversity. (shrink)

What is a larva, if it is not what survives of an ancestor's adult, compressed into a transient pre‐reproductive phase, as suggested by Haeckel's largely disreputed model of evolution by recapitulation? A recently published article hypothesizes that larva and adult of holometabolous insects are developmental expressions of two different genomes coexisting in the same animal as a result of an ancient hybridization event between an onychophoran and a primitive insect with eventless post‐embryonic development. More likely, however, larvae originated from late (...) embryonic or early post‐embryonic stages of ancestors with direct development. Evolutionary novelties would thus be intercalary rather than terminal, with respect to the ancestor's ontogenetic schedule. This scenario, supported by current research on holometabolous insects and marine invertebrates with complex life cycles, offers a serious alternative to the traditional scenario (‘what is early in ontogeny is also early in phylogeny’) underlying the current perception of the evolution of genetic regulatory networks. (shrink)

Because of the steady involvement of organisms in evolutionary dynamics, of the frequent occurrence of uniparental reproduction and of the diverse outcome of hybridisation events, the species category does not easily apply to a sizeable part of the living world. Problematic is also often the use of the category of the individual, especially in the case of polyembryony, and the distinction between metamorphosis of the individual and metagenesis (alternation of generations) is also often uncertain. More generally, fixing origins is commonly (...) arbitrary, in respect to phylogeny (‘origin’ of species) and ontogeny (‘origin’ of individual) alike. (shrink)

Is it possible, and in the first place is it even desirable, to define what "development" means and to determine the scope of the field called "developmental biology"? Though these questions appeared crucial for the founders of "developmental biology" in the 1950s, there seems to be no consensus today about the need to address them. Here, in a combined biological, philosophical, and historical approach, we ask whether it is possible and useful to define biological development, and, if such a definition (...) is indeed possible and useful, which definition can be considered as the most satisfactory. (shrink)

This study analyzes shells of marine gastropods of a zoological museum and the Latin epithets expressing perceptual and connotative attributes that they have received in the standard, Linnaean nomenclature. Making use of the Osgood semantic differential, we presented the subjects with digital 3-D reproductions of the shell specimens to be subjectively evaluated according to 17 pairs of attributes. The results show that, overall, the subjective evaluations given by the subjects are consistent, which suggests that an intersubjective characterization of the shells (...) as wholes according to their qualitative and morphological traits is possible and scientifically explicable. This may apply to other biological items as well. The results also show that the epithets given to the shells by taxonomists do not always reflect the perceptual evaluation of the general population, being a product of the well-known ambiguity in taxonomic categorization and naming. (shrink)

Edited by Alessandro Minelli and Thomas Pradeu, Towards a Theory of Development gathers essays by biologists and philosophers, which display a diversity of theoretical perspectives. The discussions not only cover the state of art, but broaden our vision of what development includes and provide pointers for future research. Interestingly, all contributors agree that explanations should not just be gene-centered, and virtually none use design and other engineering metaphors to articulate principles of cellular and organismal organization. I comment in (...) particular on the issue of how to construe the notion of a ‘theory’ and whether developmental biology has or should aspire to have theories, which four of the contributions discuss in detail while taking opposing positions. Beyond construing a theory in terms of its empirical content, my aim is to shift the focus toward the role that theories have for guiding future scientific theorizing and practice. Such a conception of ‘theory’ is particularly important in the context of development, because arriving at a theoretical framework that provides guidance for the discipline of developmental biology as a whole is more plausible than a unified representation of development across all taxa. (shrink)

Preface Phillip R. Sloan, Gerald McKenny, Kathleen Eggleson pp. xiii-xviii In November of 2009, the University of Notre Dame hosted the conference “Darwin in the Twenty-First Century: Nature, Humanity, and God.‘ Sponsored primarily by the John J. Reilly Center for Science, Technology, and Values at Notre Dame, and the Science, Theology, and the Ontological Quest project within the Vatican Pontifical... 1. Introduction: Restructuring an Interdisciplinary Dialogue Phillip R. Sloan pp. 1-32 Almost exactly fifty years before the Notre Dame conference, the (...) world’s largest centenary commemoration of Darwin’s legacy was held at nearby University of Chicago. This event, organized by a committee spearheaded by University of Chicago anthropologist Sol Tax, drew nearly 2,500 registrants. In attendance were the primary leaders... Part 1. Nature 2. Evolution through Developmental Change: How Alterations in Development Cause Evolutionary Changes in Anatomy Scott F. Gilbert pp. 35-60 For the past half-century, the mechanisms of evolution have been explained by the fusion of genetics and evolutionary biology called “the Modern Synthesis.‘ The tenets of the Modern Synthesis have been generally formulated as such: 1. There is genetic variation within the population. 2. There is competition... 3. The Evolution of Evolutionary Mechanisms: A New Perspective Stuart A. Newman pp. 61-89 The Modern Evolutionary Synthesis, based on Charles Darwin’s concept of natural selection in conjunction with a genetic theory of inheritance in a population-based framework, has been, for more than six decades, the dominant scientific perspective for explaining the diversity of living organisms. In recent years, however, with the growth... 4. The Evolvability of Organic Forms: Possible, Likely, and Unlikely Change from the Perspective of Evolutionary Developmental Biology Alessandro Minelli pp. 90-115 Confronted with the extraordinary diversity of animal form, we can ask questions about function and adaptation. How does this animal move? How does it feed? How does it defend itself from its enemies? But we can also ask questions about development, reproduction, and heredity. What mechanisms produce these forms? How are these... 5. Accident, Adaptation, and Teleology in Aristotle and Darwinism David J. Depew pp. 116-143 Charles Darwin framed the Origin of Species to meet criteria for inductive science set out by John Herschel in his Preliminary Discourse on the Study of Natural Philosophy. Accordingly, he was distraught when he learned that Herschel, to whom he had sent a copy of his newly published book, was not... 6. The Game of Life Implies Both Teleonomy and Teleology Gennaro Auletta, Ivan Colagè, Paolo D’Ambrosio pp. 144-164 The present contribution is mainly aimed at suggesting the importance of teleonomy and teleology as explanatory mechanisms in biology in the light of recent achievements in the field, and at showing that they play an actual and relevant role in the realm of life. The issue of finality in biology still provokes lively debates in the... Part 2. Humanity 7. Humanity’s Origins Bernard Wood pp. 167-181 One of Charles Darwin’s many achievements is that he began the process of converting the Tree of Life from a religious metaphor into a biological reality. All types of living organisms, be they animals, plants, fungi, bacteria, or viruses, are at the end of twigs that reach the surface of the Tree of Life, and all the types of organisms... 8. Darwin’s Evolutionary Ethics: The Empirical and Normative Justifications Robert J. Richards pp. 182-200 In the increasingly secular atmosphere of the nineteenth century, intellectuals grew wary of the idea that nature had any moral authority. In an earlier age, one might have looked upon the dispositions of nature as divinely sanctioned, and thus one could call upon natural law to ground moral judgment. Certain behaviors, for instance, might have... 9. Crossing the Milvian Bridge: When Do Evolutionary Explanations of Belief Debunk Belief? Paul E. Griffiths, John S. Wilkins pp. 201-231 Two traditional targets for evolutionary skepticism are religion and morality. Evolutionary skeptical arguments against religious belief are continuous with earlier genetic arguments against religion, such as that implicit in David Hume’s Natural History of Religion. Evolutionary arguments are also... 10. Questioning the Zoological Gaze: Darwinian Epistemology and Anthropology Phillip R. Sloan pp. 232-266 This quotation from Darwin’s Descent of Man illuminates an under-explored issue in Darwin’s work---not the issue of evolutionary ethics itself, but the epistemology of experience assumed in his work, and the consequences of his application of this “zoological gaze‘ to human beings. I will term this epistemological stance in this chapter “natural historical... Part 3. God 11. Evolution and Catholic Faith John O’Callaghan pp. 269-298 To begin to examine the relation of orthodox Catholic Christian faith to evolutionary theory and the question of human origins, consider words of the fourth pope, St. Clement: Let us fix our gaze on the Father and Creator of the whole world, and let us hold on to his peace and blessings, his splendid and surpassing... 12. After Darwin, Aquinas: A Universe Created and Evolving William E. Carroll pp. 299-337 At the 2000 Jubilee Session for scientists, held at the Vatican in May of that year, Archbishop Józef Życiński offered an eloquent assessment of contemporary discourse on the relationship between the natural sciences and theology. He ended his address with the comment that what is needed today is a new Thomas Aquinas. I remember... 13. Evolutionary Theism and the Emergent Universe Józef Życiński pp. 338-354 The 150th anniversary of the publication of Charles Darwin’s The Origin of Species has been celebrated in the context of an animated debate concerning both scientific and philosophical issues implied by the theory of evolution.1 One finds a deep diversity of attitudes, both methodological and semantic, in the current debates on evolutionary... 14. Beyond Separation or Synthesis: Christ and Evolution as Theodrama Celia Deane-Drummond pp. 355-380 The fervor with which popular discourse on science and religion has continued to bubble up in the anniversary year celebrating Darwin’s achievements shows that the publically perceived conflict between science and religion will not go away. Academic discussion on such matters is therefore not just peripheral to cultural concerns but takes... Part 4. Past and Future Prospects 15. Imagining a World without Darwin Peter J. Bowler pp. 383-403 What would have happened if Charles Darwin had not lived to write On the Origin of Species? Perhaps his bad health caused the early death he feared, or maybe he fell overboard while on the voyage of the Beagle. Would the world have still experienced the Darwinian Revolution under another name, or would the history of science, and... 16. What Future for Darwinism? Jean Gayon pp. 404-423 What future for Darwinism? I will propose some criteria for exploring this question in the domains of both evolutionary biology and the human sciences. Do not expect me to tell you where we will stand thirty years from now. It will be enough to identify a few general tendencies. For the sake of brevity, I will not devote a preamble to explain... Contributors pp. 424-430. (shrink)

We show that the semi-linear ordering principle for continuous functions implies the determinacy of all Wadge and Lipschitz games.

Zygon®, Volume 56, Issue 4, Page 1058-1069, December 2021.

We prove that the determinacy of all Lipschitz games, the determinacy of all Wadge games, and the semi-linear ordering principle for Lipschitz maps are all equivalent.

In this brief discussion, we explicate and evaluate Heyes and colleagues’ deflationary approach to interpreting apparent evidence of domain-specific processes for social percep- tion. We argue that the deflationary approach sheds important light on how functionally specific processes in social perception can be subserved at least in part by domain-general processes. On the other hand, we also argue that the fruitfulness of this approach has been unnecessarily hampered by a contrastive conception of the relationship between domain- general and domain-specific processes. (...) As an alternative, we propose a complementary conception: the identification of domain-general processes that are engaged in instances of social perception can play a positive, structuring role by adding additional constraints to be accounted for in modelling the domain-specific processes that are also involved in such instances. (shrink)

Este artículo presenta un enfoque del problema de la relación entre abducción y percepción en la filosofía de C. S. Peirce, tratando de mostrar la percepción y la abducción, o hipótesis, como procesos creativos capaces de introducir una novedad en el conocimiento. En primer lugar se muestra cómo cada conocimiento, incluso el lógico, está fundamentado en la experiencia de la percepción, y cómo esta presupone una continuidad cosmológica entre la mente y el mundo para poder funcionar. Sucesivamente se pone en (...) evidencia cómo la hipótesis no es nada más que aquel procedimiento que reconoce, como un relámpago, esta continuidad cosmológica de experiencia entre la mente y el mundo. Finalmente, la abducción se configura como un razonamiento que, libremente, obstruye y modifica el flujo continuo de. (shrink)

The theme of conspiracies plays a key role in Machiavelli's writings, in which can be found considerations and analyses on the use of conspiracy as an instrument of conquest of power, and as a technique for political fighting. This volume denies an interpretation in which Machiavelli limited himself to warning against conspiracies, judging them as a dangerous and useless tool. In reality, he elaborated a real phenomenology or anatomy of the conspiracy. His thoughts on this theme represent a practical manual (...) for the "coup d'état" and the violent seizure of power. But as always, they also contain brilliant intuitions on political psychology, the sociology of power, and social anthropology. (shrink)

Alfred North Whitehead famously compares the philosophical method of knowledge acquisition with the process of flying an airplane. Likewise, “shamanic flight” marks stages of cognitive processing in navigation through perceptible and imperceptible worlds. This article focuses on the cosmovision of the Amazon people Huni Kuin, the Whiteheadian method of imaginative rationalization, and the concept of Amerindian perspectivism. This study also investigates shamanism as an experience of knowledge generation. Furthermore, “shamanic flight,” as an ecstatic technique experienced in many diverse Amerindian rituals, (...) will be explored as a method in the discovery and organization of nonhuman alterities. Finally, Amazonian-based shamanic epistemology will be discussed within a “multinaturalist” ontology. (shrink)

Whiteheadian concepts of life, food, "empty" and "occupied space" provide a theoretical basis to unpack an ontogenetic perspective on aging. Focusing on the so-called "Selective Optimization with Compensation " strategy, this work will explore this concept in relation to some scientific evidence in the fields of "epigenetics " and molecular nutrition. Further, the role of caloric restriction in health and longevity will be discussed as a SOC strategy, based on the metabolic theory of aging. SOC strategy applied to the processes (...) of aging, when linked with Whitehead's philosophy of organism, makes it possible for us to think about life as a selective process provided by "empty space. " A continuum within the physical field optimizes a "living society," which evolves in permanent social deficit, by means of compensation by nutritional metabolism. (shrink)

Most model checking techniques for security protocols make a number of simplifying assumptions on the protocol and/or on its execution environment that greatly complicate or even prevent their applicability in some important cases. For instance, most techniques assume that communication between honest principals is controlled by a Dolev-Yao intruder, i.e. a malicious agent capable to overhear, divert, and fake messages. Yet we might be interested in establishing the security of a protocol that relies on a less unsecure channel (e.g. a (...) confidential channel provided by some other protocol sitting lower in the protocol stack). In this paper we propose a general model for security protocols based on the set-rewriting formalism that, coupled with the use of LTL, allows for the specification of assumptions on principals and communication channels as well as of complex security properties that are normally not handled by state-of-the-art security protocol analysers. By using our approach we have been able to formalise all the assumptions required by the ASW protocol for optimistic fair exchange and some of its key security properties. Besides the previously reported attacks on the protocol, we report a new attack on a patched version of the protocol. (shrink)

O propósito deste artigo é mostrar a relação entre a experiência perceptiva e o raciocínio abdutivo em C.S. Peirce. Ademais, apresento a abdução como uma expressão lógica, prática e criativa apta a introduzir uma novidade no reino do conhecimento, através de um sistema de signos gráficos. A noção peirciana de experiência está relacionada com a de uma práxis interpretativa e criativa, que não se limita ao recebimento ou registro de dados pré-constituídos passivamente. Nesse sentido, a abdução é o hábito lógico (...) vivo que explica o mundo percebido como um caso particular de um mundo concebível, no qual uma regra geral ou hipótese é efetivo. Apresentarei a abdução como um raciocínio que infere a causa a partir do efeito, o antecedente a partir do consequente, a ordem geral de um fato percebido particular e um “extra comum”. A abdução não apenas estabelece um fato singular, mas torna o fato visível dentro de um novo contexto de relações possíveis. Assim, quando vemos uma figura, nós não vemos somente uma mera figura, mas uma figura “como se” ela fosse o resultado percebido de um sistema geral de relações possíveis. O gesto da mão dá existência à figura e a torna visível para nós, pois ela descobre essas relações que constituem o contexto de interpretação da figura. Nesse aspecto, o gesto gráfico consiste na concretização prática que permite uma interpretação topológica possível do mundo real percebido. (shrink)

Wittgenstein has written a great number of remarks relevant to aesthetical issues: he has questioned the relation between aesthetics and psychology as well as the status of our norms of judgment; he has drawn philosophers attention to such topics as aspect-seeing and aspect-dawning, and has brought insights into the nature of our aesthetic reactions. The examination of this wide range of topics is far from being completed, and the purpose of this book is to contribute to such completion. It gathers (...) both papers discussing some of Wittgenstein s most provocative and intriguing statements on aesthetics, and papers bringing out their implications for art critic and art history, as well as their significance to epistemology and to the study of human mind.". (shrink)

Assuming AD + DC, we characterize the self-dual boldface pointclasses which are strictly larger than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank [Formula: see text], and those of Wadge rank [Formula: see text] when ξ is limit.

By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal "infinitesimal subgroup" G00 such that the quotient G/G00, equipped with the "logic topology", is a compact (real) Lie group. Our first result is that the functor G → G/G00 sends exact sequences of definably compact groups into exact sequences of Lie groups. We then study the connections between the Lie group G/G00 and the o-minimal spectrum (...) G̃ of G. We prove that G/G00 is a topological quotient of G̃. We thus obtain a natural homomorphism ψ* from the cohomology of G/G00 to the (Čech-)cohomology of G̃. We show that if G00 satisfies a suitable contractibility conjecture then $\widetilde{G^{00}}$ is acyclic in Čech cohomology and ψ* is an isomorphism. Finally we prove the conjecture in some special cases. (shrink)

L’articolo intende sondare la fondatezza ontologica di una categoria personologica fondamentale, in particolare in ambito ecclesiologico: il “noi”. Tale ricerca si sviluppa soprattutto nella sua rilevanza trinitaria, a partire dall’apporto offerto dal teologo tedesco Heribert Mühlen, il quale, nella sua opera pneumatologica Der Heilige Geist als Person. In der Trinität, bei der Inkarnation und im Gnadenbund: Ich-Du-Wir, approfondisce questo tema insieme ad altre tre parole-chiave: “io”, “tu”, “tra”.

The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated (...) and invariant under elementary extensions and expansions of the language. (shrink)

The axiom of dependent choice ( $\mathsf {DC}$ ) and the axiom of countable choice ( ${\mathsf {AC}}_\omega $ ) are two weak forms of the axiom of choice that can be stated for a specific set: $\mathsf {DC} ( X )$ asserts that any total binary relation on X has an infinite chain, while ${\mathsf {AC}}_\omega ( X )$ asserts that any countable collection of nonempty subsets of X has a choice function. It is well-known that $\mathsf {DC} \Rightarrow (...) {\mathsf {AC}}_\omega $. We study for which sets and under which hypotheses $\mathsf {DC} ( X ) \Rightarrow {\mathsf {AC}}_\omega ( X )$, and then we show it is consistent with $\mathsf {ZF}$ that there is a set $A \subseteq \mathbb {R}$ for which $\mathsf {DC} ( A )$ holds, but ${\mathsf {AC}}_\omega ( A )$ fails. (shrink)

We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.