We study generalized amalgamation properties in simple theories. We formulate a notion of generalized amalgamation in such a way so that the properties are preserved when we pass from T to Teq or Theq; we provide several equivalent ways of formulating the notion of generalized amalgamation.We define two distinct hierarchies of simple theories characterized by their amalgamation properties; examples are given to show the difference between the hierarchies.

Cancer research is experiencing ‘paradigm instability’, since there are two rival theories of carcinogenesis which confront themselves, namely the somatic mutation theory and the tissue organization field theory. Despite this theoretical uncertainty, a huge quantity of data is available thanks to the improvement of genome sequencing techniques. Some authors think that the development of new statistical tools will be able to overcome the lack of a shared theoretical perspective on cancer by amalgamating as many data as possible. We think instead (...) that a deeper understanding of cancer can be achieved by means of more theoretical work, rather than by merely accumulating more data. To support our thesis, we introduce the analytic view of theory development, which rests on the concept of plausibility, and make clear in what sense plausibility and probability are distinct concepts. Then, the concept of plausibility is used to point out the ineliminable role played by the epistemic subject in the development of statistical tools and in the process of theory assessment. We then move to address a central issue in cancer research, namely the relevance of computational tools developed by bioinformaticists to detect driver mutations in the debate between the two main rival theories of carcinogenesis. Finally, we briefly extend our considerations on the role that plausibility plays in evidence amalgamation from cancer research to the more general issue of the divergences between frequentists and Bayesians in the philosophy of medicine and statistics. We argue that taking into account plausibility-based considerations can lead to clarify some epistemological shortcomings that afflict both these perspectives. (shrink)

We show that in a stable first-order theory, the failure of higher dimensional type amalgamation can always be witnessed by algebraic structures that we call n-ary polygroupoids. This generalizes a result of Hrushovski in [16] that failures of 4-amalgamation are witnessed by definable groupoids. The n-ary polygroupoids are definable in a mild expansion of the language.

We prove a couple of results on NTP2 theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by 2. This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP2 theories based on S1 ideals with amalgamation and ask some questions. We then define and study a class of groups with generically simple generics, generalizing NIP groups with generically stable generics.

There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum–Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andréka–Németi–Sain. It is also shown (...) that given the mentioned extra assumptions the Robinson property implies the interpolation property. As conditionally algebraizable logics cover algebraizable logics as well as various quantifier logics such as classical first order logic, our results yield a generalization of some of the results concerning interpolation and amalgamation. (shrink)

In this article we discuss a version of the Robinson property studied recently by Gyenis in, and we present a solution to one of his open problems. We say that a first‐order structure satisfies the Robinson property whenever the union of two non‐trivial partial n‐types over different finite sets is realizable if and only if they are not explicitly contradictory. In his article, Gyenis showed that a universal, homogeneous structure over a language that consists of at most binary relation symbols (...) satisfies the Robinson property if and only if its age has a generalized amalgamation property (the so called prescribed amalgamation property, PAP). We go further and define a series of new kinds of amalgamation properties, APn for any natural number n. Using these properties we can characterize all universal and homogeneous structures that satisfy the Robinson property independently from the arities of relation symbols of the language. (shrink)

In this paper, we introduce the notion of $${\textbf{K}} $$ -rank, where $${\textbf{K}} $$ is a strong amalgamation Fraïssé class. Roughly speaking, the $${\textbf{K}} $$ -rank of a partial type is the number “copies” of $${\textbf{K}} $$ that can be “independently coded” inside of the type. We study $${\textbf{K}} $$ -rank for specific examples of $${\textbf{K}} $$, including linear orders, equivalence relations, and graphs. We discuss the relationship of $${\textbf{K}} $$ -rank to other ranks in model theory, including dp-rank (...) and op-dimension (a notion coined by the first author and C. D. Hill in previous work). (shrink)

It is argued in this paper that amalgamating confirmation from various sources is relevantly different from social-choice contexts, and that proving an impossibility theorem for aggregating confirmation measures directs attention to irrelevant issues.

Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local (...) deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open. (shrink)

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure M, Polish group G of permutations of M, and \, G has a comeager n-diagonal conjugacy class iff the family of all n-tuples of G-extendable bijections between finitely generated substructures of M, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not (...) homogenizable. Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces. (shrink)

This paper is devoted to the proof of the following upward categoricity theorem: Let K be a tame abstract elementary class with amalgamation, arbitrarily large models, and countable Löwenheim-Skolem number. If K is categorical in ‮א‬₁ then K is categorical in every uncountable cardinal. More generally, we prove that if K is categorical in a successor cardinal λ⁺ then K is categorical everywhere above λ⁺.

\(\nabla \) -algebra is a natural generalization of Heyting algebra, unifying many algebraic structures including bounded lattices, Heyting algebras, temporal Heyting algebras and the algebraic presentation of the dynamic topological systems. In a series of two papers, we will systematically study the algebro-topological properties of different varieties of \(\nabla \) -algebras. In the present paper, we start with investigating the structure of these varieties by characterizing their subdirectly irreducible and simple elements. Then, we prove the closure of these varieties under (...) the Dedekind-MacNeille completion and provide the canonical construction and the Kripke representation for \(\nabla \) -algebras by which we establish the amalgamation property for some varieties of \(\nabla \) -algebras. In the sequel of the present paper, we will complete the study by covering the logics of these varieties and their corresponding Priestley-Esakia and spectral duality theories. (shrink)

In this paper we make an attempt to study classes of models by using general logics. We do not believe that Lww is always the best logic for analyzing a class of models. Let K be a class of models and L a logic. The main assumptions we make about K and C are that K has the L-amalgamation property and, later in the paper, that K does not omit L-types. We show that, if modified suitably, most of the (...) results of stability theory hold in this context. The main difference is that existentially closed models of K play the role that arbitrary models play in traditional stability theory. We prove e. g. a structure theorem for the class of existentially closed models of K assuming that K is a trivial superstable class with ndop. (shrink)

Generalizedn-gons are certain geometric structures (incidence geometries) that generalize the concept of projective planes (the nontrivial generalized 3-gons are exactly the projective planes).In a simplified world, every generalizedn-gon of finite Morley rank would be an algebraic one, i.e., one of the three families described in [9] for example. To our horror, John Baldwin [2], using methods discovered by Hrushovski [7], constructed ℵ1-categorical projective planes which are not algebraic. The projective planes that Baldwin constructed fail to be algebraic in a (...) dramatic way.Indeed, every algebraic projective plane over an algebraically closed field is Desarguesian [12]. In particular, an algebraically closed field (isomorphic to the base field) can be interpreted in every one of them. However, in the projective planes that Baldwin constructed, one cannot even interpret an infinite group.In this article we show that the same phenomenon occurs for the generalizedn-gons ifn≥ 3 is an odd integer. For each suchnwe constructmany nonisomorphic generalizedn-gons of finite Morley rank that do not interpret an infinite group. As one may expect, our method is inspired by Hrushovski and Baldwin, and we follow Baldwin's line of approach. Quite often our proofs are a verification of the fact that the proofs of Baldwin [2] forn= 3 carry over to an arbitrary positive odd integern(which is sometimes far from being obvious). As in [2], we begin by defining a certain collection of finite graphsK* and a binary relation ≤ on these graphs. We show that (K*, ≤) satisfies the amalgamation property. (shrink)

We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than (...) truth degree. We study n-nuanced MV-algebras mainly from the algebraic and categorical points of view, and also consider some basic model-theoretic aspects. The relationship with a suitable notion of n-nuanced ordered group via an extension of the Γ construction is also analyzed. (shrink)

LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a generic automorphism. In (...) the present paper we give a weaker condition of this kind which is equivalent to the existence of generic automorphisms. Really we give more: a characterization of the existence of generic expansions (defined in an appropriate way) of an ω-categorical structure. We also show that Truss' condition guarantees the existence of a countable structure consisting of automorphisms ofMwhich can be considered as an atomic model of some theory naturally associated toM. We do it in a general context of weak models for second-order quantifiers.The author thanks Ludomir Newelski for pointing out a mistake in the first version of Theorem 1.2 and for interesting discussions. Also, the author is grateful to the referee for very helpful remarks. (shrink)

Le général André Bach dans une réflexion sur l’« horizon de mort dans la violence de guerre » part d’une approche anthropologique du phénomène de violence et de la peur (quasiment biologique) qu’il engendre en soulignant les difficultés des sociétés occidentales à penser la mort. C’est l’État qui donne à la guerre un sens politique et sacré et qui crée les catégories fonctionnelles de la guerre (les concepts de paix et de guerre ne sont pas en eux-mêmes opérationnels). Dans le (...) cadre d’une réflexion clausewitzienne sur la montée aux extrêmes, l’« extrême » pour le soldat est toujours sa propre mort (plus que celle de l’ennemi). Les notions de barbarisation et humanisation ne peuvent en ce sens rendre compte de la violence et de la peur radicales présentes dans toute guerre où le rôle du commandement est toujours de mettre en œuvre un degré de violence supérieur à celui de l’adversaire, sans aucune considération de « proportionnalité » de cette violence. La mise à distance technique ne diminue pas la violence mais l’augmente à proportion de l’éloignement de la peur. Seul le politique peut et doit mettre des limites à cette violence militaire par nature illimitée. La modernisation des armes ne relève jamais d’une humanisation du combat mais d’une recherche d’une violence plus efficace. L’entraînement du soldat en temps de paix n’est jamais entraînement à la violence mais apprentissage de savoir-faire et effort de constitution d’un groupe soudé, doté d’un bon moral. L’ordre et la formation tentent de limiter la sauvagerie mais il existe une constitution endogène de comportements propres au soldat, que la hiérarchie tente de canaliser dans une symbolique guerrière fondée sur le sentiment de l’honneur (destiné à compenser la peur d’être une proie vouée à mourir et à faire préférer la lutte au coude à coude sur l’instinct de conservation). Le couple violence/honneur fait que l’armée dépourvue de contrat social n’est pas soluble dans le politique (aujourd’hui dans les écoles militaires on ne parle plus d’« honneur » mais d’« éthique »…, mais pour dire la même chose). La conscription fut une rupture de la logique endogène de l’armée et introduisit une brèche dans ce système archaïque. Mais religion (au Moyen Âge) ou logique démocratique (de nos jours) s’avèrent surtout des « béquilles idéologiques » qui, en définitive, sont souvent plus efficaces pour accroître la barbarisation que pour l’éviter (exemple de la colonisation algérienne où une armée de paix, fonctionnarisée et rigoureusement canalisée, appartenant à une génération n’ayant jamais connu de violence de guerre, développe des massacres de masse). (shrink)

Écriture sans écriture, critique sans discours : il s’agit de traquer et de faire ressortir l’obsession du « projet » et de son idéologie dans la trame d’un appel à contrats doctoraux. Ctrl+B chaque fois (et elles sont très nombreuses) où le petit mot est réitéré.

The publication of the article “Recent Models of the African Iron Age and the Cattle-Related Evidence” by Hromnik in a journal sponsored by Unesco raises a number of serious issues which we, as members of the International Scientific Committee charged with the responsibility of preparing an up-to-date and scientific history of Africa purged of its mists of racist propaganda, unfounded assertions and misleading and dangerous misinterpretations, cannot ignore. These issues include the scientific accuracy or authenticity of the article.

Source: Author: Leonila C. Crisostomo, Ma. Teresa G. Generales, Amelita L. de Guzman The primary purpose of this study is to ascertain the benefits of the National Service Training Program implementation and to identify the problems encountered by its implementers. Results showed that the benefits derived from the program were topped by enhancement of skills on basic leadership with emphases on the ability to listen and ability to communicate which were rated very important and very much benefited among other training (...) aspects of the program. Results also revealed that students are aware of the importance of physical, mental and social health as well as the observance of proper hygiene for overall sense of well-being. Although recreation is one aspect that the respondents find important, appreciation of it underscores the need to have more time for assignments and projects as most of the respondents are enrolled in their respective courses with 29 units, making them unable to appreciate the perks of involving themselves into various recreational activities. Problems in the implementation showed lack of provision of materials and equipment and of budgetary allocation which rendered full implementation weak as students and faculty involved in the community immersion have to rely on their own resources, in addition to the indifference and passivity of the local government officials. Based on the findings, the researchers recommended that: the school administrators need to allocate adequate budget for materials and equipment; periodic faculty development trainings and; to look into the passive attitude of the local officials to ensure that implementation NSTP projects will benefit both clients and implementers. ]]>. (shrink)