We study Martsinkovsky–Russell torsion modules with pure embeddings as an abstract elementary class. We give a model-theoretic characterization of the pure-injective and the Σ-pure-injective modules relative to the class of torsion modules assuming that the torsion submodule is a pure submodule. Our characterization of relative Σ-pure-injective modules extends the classical characterization of Gruson and Jenson as well as Zimmermann. We study the limit models of the class and determine when the class is superstable (...) assuming that the torsion submodule is a pure submodule. As a corollary, we show that the class of torsion abelian groups with pure embeddings is strictly stable (i.e., stable not superstable). (shrink)

We show that certain classes of modules have universal models with respect to pure embeddings: Let R be a ring, T a first‐order theory with an infinite model extending the theory of R‐modules and (where ⩽pp stands for “pure submodule”). Assume has the joint embedding and amalgamation properties. If or, then has a universal model of cardinality λ. As a special case, we get a recent result of Shelah [28, 1.2] concerning the existence of universal reduced torsion‐free (...) abelian groups with respect to pure embeddings.We begin the study of limit models for classes of R‐modules with joint embedding and amalgamation. We show that limit models with chains of long cofinality are pure‐injective and we characterize limit models with chains of countable cofinality. This can be used to answer [18, Question 4.25].As this paper is aimed at model theorists and algebraists an effort was made to provide the background for both. (shrink)

Fisher [10] and Baur [6] showed independently in the seventies that if T is a complete first-order theory extending the theory of modules, then the class of models of T with pure embeddings is stable. In [25, 2.12], it is asked if the same is true for any abstract elementary class $(K, \leq _p)$ such that K is a class of modules and $\leq _p$ is the pure submodule relation. In this paper we give some instances where this (...) is true:Theorem.Assume R is an associative ring with unity. Let $(K, \leq _p)$ be an AEC such that $K \subseteq R\text {-Mod}$ and K is closed under finite direct sums, then: •If K is closed under pure-injective envelopes, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda \geq \operatorname {LS}(\mathbf {K})$ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•If K is closed under pure submodules and pure epimorphic images, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•Assume R is Von Neumann regular. If $\mathbf {K}$ is closed under submodules and has arbitrarily large models, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.As an application of these results we give new characterizations of noetherian rings, pure-semisimple rings, Dedekind domains, and fields via superstability. Moreover, we show how these results can be used to show a link between being good in the stability hierarchy and being good in the axiomatizability hierarchy.Another application is the existence of universal models with respect to pure embeddings in several classes of modules. Among them, the class of flat modules and the class of $\mathfrak {s}$ -torsion modules. (shrink)

Van den Dries, L. and J. Holly, Quantifier elimination for modules with scalar variables, Annals of Pure and Applied Logic 57 161–179. We consider modules as two-sorted structures with scalar variables ranging over the ring. We show that each formula in which all scalar variables are free is equivalent to a formula of a very simple form, uniformly and effectively for all torsion-free modules over gcd domains . For the case of Presburger arithmetic with scalar variables (...) the result takes a still simpler form, and we derive in this way the polynomial-time decidability of the sets defined by such formulas. (shrink)

We investigate the issues of Diophantine definability over the non-finitely generated version of non-degenerate modules contained in the infinite algebraic extensions of the rational numbers. In particular, we show the following. Let k be a number field and let K inf be a normal algebraic, possibly infinite, extension of k such that k has a normal extension L linearly disjoint from K inf over k. Assume L is totally real and K inf is totally complex. Let M inf be (...) a non-degenerate O k -module, possibly non-finitely generated and contained in O Kinf . Then M inf contains a submodule M¯ inf such that M inf /M¯ inf is torsion and O k has a Diophantine definition over M¯ inf. (shrink)

Ulm’s Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to L∞ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty \omega }$$\end{document}-equivalence. In this paper, we extend this classification to a class of mixed Zp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_p$$\end{document}-modules which includes all Warfield modules and is closed under L∞ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty \omega }$$\end{document}-equivalence. The defining property of these modules is the existence of what we call a partial decomposition basis, a generalization of the concept of decomposition basis. We prove a complete classification theorem in L∞ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\infty \omega }$$\end{document} using invariants deduced from the classical Ulm and Warfield invariants. (shrink)

We prove an Ax-Kochen-Ershov like transfer principle for groups acting on groups. The simplest case is the following: let B be a soluble group acting on an abelian group G so that G is a torsion-free divisible module over the group ring Z[B], then the theory of B determines the one of the two-sorted structure $\langle G, B, *\rangle$ , where * is the action of B on G. More generally, we show a similar principle for structures $\langle G, (...) B, *\rangle$ , where G is a torsion-free divisible module over the quotient of Z[B] by the annulator of G. Two applications come immediately from this result: First, for not necessarily commutative domains, where we consider the action of a subgroup of the invertible elements on the additive group. We obtain then the decidability of a weakened structure of ring, with partial multiplication. The second application is to pure groups. The semi-direct product of G by B is bi- interpretable with our structure $\langle G, B, *\rangle$ . Thus, we obtain stable decidable groups that are not linear over a field. (shrink)

For arbitrary finite group $G$ and countable Dedekind domain $R$ such that the residue field $R/P$ is finite for every maximal $R$ -ideal $P$ , we show that the localizations at every maximal ideal of two $RG$ -lattices are isomorphic if and only if the two lattices satisfy the same first order sentences. Then we investigate generalizations of the above results to arbitrary $R$ -torsion-free $RG$ -modules and we apply the previous results to show the decidability of the (...) theory of ${\vec Z}C(2)^2$ -lattices. Eventually, we show that ${\vec Z} [i] C(2)^2$ -lattices have undecidable theory. (shrink)

The point of view expressed in the present research is directed towards the ideational “torsion” from rationalism to the “language-games” drawing up an analysis according to which one can notice the rationalist and post-rationalist aspects in the philosophy of communication, and the consequences of these perspectives, which could be of great interest as regards the philosophical concepts related to communication, to man or to the human community. As a matter of fact, “the torsion” is only apparent; it cannot (...) hold a dramatic change of the thinking range, from “rationalism” to “neo-positivism”, as regards the comment on Habermas’ theory of communication, as compared to Wittgenstein’s ideas about “the language-games” as central elements of human communication. Jürgen Habermas manifest a specific turn in his way of thinking, aiming at the contemporary modulation of the rationalist approach by means of inter-subjectivism orhumanism, and stressing the modulation of the logical approach, by means of “language-games” and “life-forms.”. (shrink)

There is a venerable philosophical tradition that views human beings as intrinsically rational, though even the most ardent defender of this view would admit that under certain circumstances people’s decisions and thought processes can be very irrational indeed. When people are extremely tired, or drunk, or in the grip of rage, they sometimes reason and act in ways that no account of rationality would condone. About thirty years ago, Amos Tversky, Daniel Kahneman and a number of other psychologists began reporting (...) findings suggesting much deeper problems with the traditional idea that human beings are intrinsically rational animals. What these studies demonstrated is that even under quite ordinary circumstances where fatigue, drugs and strong emotions are not factors, people reason and make judgments in ways that systematically violate familiar canons of rationality on a wide array of problems. Those first surprising studies sparked the growth of a major research tradition whose impact has been felt in economics, political theory, medicine and other areas far removed from cognitive science. In Section 2, we will sketch a few of the better known experimental findings in this area. We’ve chosen these particular findings because they will play a role at a later stage of the paper. For readers who would like a deeper and more systematic account of the fascinating and disquieting research on reasoning and judgment, there are now several excellent texts and anthologies available. (shrink)

(No abstract is available for this citation).

Though the realm of biology has long been under the philosophical rule of the mechanistic magisterium, recent years have seen a surprisingly steady rise in the usurping prowess of process ontology. According to its proponents, theoretical advances in the contemporary science of evo-devo have afforded that ontology a particularly powerful claim to the throne: in that increasingly empirically confirmed discipline, emergently autonomous, higher-order entities are the reigning explanantia. If we are to accept the election of evo-devo as our best conceptualisation (...) of the biological realm with metaphysical rigour, must we depose our mechanistic ontology for failing to properly “carve at the joints” of organisms? In this paper, I challenge the legitimacy of that claim: not only can the theoretical benefits offered by a process ontology be had without it, they cannot be sufficiently grounded without the metaphysical underpinning of the very mechanisms which processes purport to replace. The biological realm, I argue, remains one best understood as under the governance of mechanistic principles. (shrink)

We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries, and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion one-form, and the laplacian defined by the RCW connection is the differential generator of the Brownian motions. We extend this to the state-space of non-relativistic quantum mechanics and discuss the relation between a non-canonical quantum RCW geometry in state-space associated with the gradient of the (...) quantum-mechanical expectation value of a self-adjoint operator given by the generalized laplacian operator defined by a RCW geometry. We discuss the reduction of the wave function in terms of a RCW quantum geometry in state-space. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian motions. Thus, in this work, the Schroedinger field is a torsion generating field, both for the linear and non-linear cases. We discuss the problem of the many times variables and the relation with dissipative processes, and the role of time as an active field, following Kozyrev and a recent experiment in non-relativistic quantum systems. We associate the Hodge dual of the drift vector field with a possible angular-momentum source for the phenomenae observed by Kozyrev. (shrink)

The combined use of molecular and structural biology techniques has proved very efficient in elucidating structure‐function relationships in aminoacyl‐tRNA synthetases. Our present understanding of this family of enzymes is based on two main unifying principles: (i) division into two different classes, corresponding to two different modes of ATP binding and attachment of the activated amino acid to the last nucleotide of tRNA (either 2′OH or 3′OH of the ribose) by two different catalytic mechanisms and two structural domains with completely different (...) folding, and (ii) the modular organization into separate and additional domains that we are just beginning to understand. Sequence analysis complements very nicely existing structural, biochemical and genetic results and makes them more general, leading to verifiable predictions. (shrink)

Research ethics remains a cornerstone of the scientific enterprise as it defines the boundaries of responsible conduct of research. Our aim was to systematically identify, review and test online training courses in research ethics which could be considered most appropriate for future training at the University of Botswana. We used an evaluative tool that included both descriptive and evaluative criteria for assessing the strengths, weaknesses and appropriateness of 10 online research ethics courses which are publicly accessible. We then assembled Focus (...) Group Discussions to engage the UB community to select the best 2–3 online courses that are considered most suited for use in future training of research ethics at UB. Twenty respondents participated in three FGDs. Our findings show that there is limited research ethics training capacity in low resourced academic institutions like UB. Online training opportunities could be used to address this challenge. Our analysis reveal that out of the 10 online courses reviewed, CITI program, Family Health International, and Training and Resource in Research Ethics Evaluation have characteristics that would make them suitable for utilization in Botswana. We believe the findings from this case study will be of value to other similarly situated research institutions. (shrink)

We study the R‐torsion‐free part of the Ziegler spectrum of an order Λ over a Dedekind domain R. We underline and comment on the role of lattices over Λ. We describe the torsion‐free part of the spectrum when Λ is of finite lattice representation type.

ABSTRACT Research ethics remains a cornerstone of the scientific enterprise as it defines the boundaries of responsible conduct of research. Our aim was to systematically identify, review and test online training courses in research ethics which could be considered most appropriate for future training at the University of Botswana (UB). We used an evaluative tool that included both descriptive and evaluative criteria for assessing the strengths, weaknesses and appropriateness of 10 online research ethics courses which are publicly accessible. We then (...) assembled Focus Group Discussions (FGDs) to engage the UB community to select the best 2–3 online courses that are considered most suited for use in future training of research ethics at UB. Twenty respondents participated in three FGDs. Our findings show that there is limited research ethics training capacity in low resourced academic institutions like UB. Online training opportunities could be used to address this challenge. Our analysis reveal that out of the 10 online courses reviewed, CITI program, Family Health International, and Training and Resource in Research Ethics Evaluation have characteristics that would make them suitable for utilization in Botswana. We believe the findings from this case study will be of value to other similarly situated research institutions. (shrink)

We prove that for any computable successor ordinal of the form α = δ + 2k there exists computable torsion-free abelian group that is relatively Δα0 -categorical and not Δα−10 -categorical. Equivalently, for any such α there exists a computable TFAG whose initial segments are uniformly described by Σαc infinitary computable formulae up to automorphism, and there is no syntactically simpler family of formulae that would capture these orbits. As far as we know, the problem of finding such optimal (...) examples of Δα0-categorical TFAGs for arbitrarily large α was first raised by Goncharov at least 10 years ago, but it has resisted solution 315–356]). As a byproduct of the proof, we introduce an effective functor that transforms a 0″-computable worthy labeled tree into a computable TFAG. We expect that this techni... (shrink)

We address three issues that might be important in evaluating the validity of the planning–control model: (1) It could be artificial to distinguish between control and planning when control involves the re-planning of a new corrective submovement that overlaps with the initial response; (2) experiments involving illusions are not totally compelling; (3) selectively implicating the superior parietal lobe in movement control and the basal ganglia in movement planning, appears questionable.