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  1. Locally Definable Subgroups of Semialgebraic Groups.Elías Baro, Pantelis E. Eleftheriou & Ya’Acov Peterzil - 2019 - Journal of Mathematical Logic 20 (2):2050009.
    We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. 18 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when (...)
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  2. Definable V-Topologies, Henselianity and NIP.Yatir Halevi, Assaf Hasson & Franziska Jahnke - 2019 - Journal of Mathematical Logic 20 (2):2050008.
    We initiate the study of definable [Formula: see text]-topologies and show that there is at most one such [Formula: see text]-topology on a [Formula: see text]-henselian NIP field. Equivalently, we show that if [Formula: see text] is a bi-valued NIP field with [Formula: see text] henselian, then [Formula: see text] and [Formula: see text] are comparable. As a consequence, Shelah’s conjecture for NIP fields implies the henselianity conjecture for NIP fields. Furthermore, the latter conjecture is proved for any field admitting (...)
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  3. On Searching Explanatory Argumentation Graphs.Régis Riveret - 2020 - Journal of Applied Non-Classical Logics 30 (2):123-192.
    Cases or examples can be often explained by the interplay of arguments in favour or against their outcomes. This paper addresses the problem of finding explanations for a collection of cases where an explanation is a labelled argumentation graph consistent with the cases, and a case is represented as a statement labelling. The focus is on semi-abstract argumentation graphs specifying attack and subargument relations between arguments, along with particular complete argument labellings taken from probabilistic argumentation where arguments can be excluded. (...)
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  4. Herzberger’s Limit Rule with Labelled Sequent Calculus.Andreas Fjellstad - 2020 - Studia Logica 108 (4):815-855.
    Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger’s limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth PosFS and a neighbourhood semantics, together with the proof of the equivalence between the two semantics, we show that (...)
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  5. On Equivalence Relations Generated by Cauchy Sequences in Countable Metric Spaces.Longyun Ding & Kai Gu - 2020 - Annals of Pure and Applied Logic 171 (10):102854.
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  6. Computation and Indispensability.Jeffrey Ketland - forthcoming - Logic and Logical Philosophy:1.
    This article provides a computational example of a mathematical explanation within science, concerning computational equivalence of programs. In addition, it outlines the logical structure of the reasoning involved in explanations in applied mathematics. It concludes with a challenge that the nominalist provide a nominalistic explanation for the computational equivalence of certain programs.
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  7. Peter Ochs and the Logic of Scriptural Reasoning.Mark Randall James - forthcoming - Modern Theology.
  8. A Descriptive Main Gap Theorem.Francesco Mangraviti & Luca Motto Ros - forthcoming - Journal of Mathematical Logic:2050025.
    Answering one of the main questions of [S.-D. Friedman, T. Hyttinen and V. Kulikov, Generalized descriptive set theory and classification theory, Mem. Amer. Math. Soc. 230 80, Chap. 7], we show that there is a tight connection between the depth of a classifiable shallow theory [Formula: see text] and the Borel rank of the isomorphism relation [Formula: see text] on its models of size [Formula: see text], for [Formula: see text] any cardinal satisfying [Formula: see text]. This is achieved by (...)
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  9. Homogeneous Structures with Non-Universal Automorphism Groups.Wiesław Kubiś & Saharon Shelah - forthcoming - Journal of Symbolic Logic:1-13.
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  10. The Value of Thinking and the Normativity of Logic.Manish Oza - forthcoming - Philosophers' Imprint.
    (1) This paper is about how to build an account of the normativity of logic around the claim that logic is constitutive of thinking. I take the claim that logic is constitutive of thinking to mean that representational activity must tend to conform to logic to count as thinking. (2) I develop a natural line of thought about how to develop the constitutive position into an account of logical normativity by drawing on constitutivism in metaethics. (3) I argue that, while (...)
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  11. The Ketonen Order.Gabriel Goldberg - forthcoming - Journal of Symbolic Logic:1-20.
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  12. Coding in Graphs and Linear Orderings.Julia F. Knight, Alexandra A. Soskova & Stefan V. Vatev - forthcoming - Journal of Symbolic Logic:1-18.
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  13. The Complexity of Homeomorphism Relations on Some Classes of Compacta.Paweł Krupski & Benjamin Vejnar - forthcoming - Journal of Symbolic Logic:1-19.
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  14. Deciding Some Maltsev Conditions in Finite Idempotent Algebras.Alexandr Kazda & Matt Valeriote - forthcoming - Journal of Symbolic Logic:1-24.
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  15. God, Incarnation in the Feminine, and the Third Presence.Lenart Škof - 2020 - Sophia 59 (1):95-112.
    This paper deals with the possibility of an incarnation in the feminine in our age. In the first part, we discuss sexual genealogies in ancient Israel and address the problem of the extreme vulnerability of feminine life in the midst of an ancient sacrificial crisis. The second part opens with an analysis of Feuerbach’s interpretation of the Trinity. The triadic logic, as found within various religious contexts, is also affirmed. Based on our analyses from the first and the second part, (...)
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  16. On the Diagonal Lemma of Gödel and Carnap.Saeed Salehi - forthcoming - Bulletin of Symbolic Logic:1-8.
    A cornerstone of modern mathematical logic is the diagonal lemma of Gödel and Carnap. It is used in e.g. the classical proofs of the theorems of Gödel, Rosser and Tarski. From its first explication in 1934, just essentially one proof has appeared for the diagonal lemma in the literature; a proof that is so tricky and hard to relate that many authors have tried to avoid the lemma altogether. As a result, some so called diagonal-free proofs have been given for (...)
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  17. Leibnizian Identity and Paraconsistent Logic.Ali Abasnezhad - 2020 - History and Philosophy of Logic 41 (3):236-243.
    The standard Leibnizian view of identity allows for substitutivity of identicals and validates transitivity of identity within classical semantics. However, in a series of works, Graham Priest argues that Leibnizian identity invalidates both principles when formalized in paraconsistent semantics. This paper aims to show the Leibnizian view of identity validates substitutivity of identicals and transitivity of identity whether the logic is classical or paraconsistent. After presenting Priest's semantics of identity, I show what a semantic expression of Leibnizian identity does amount (...)
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  18. Weyl Reexamined: “Das Kontinuum” 100 Years Later.Arnon Avron - forthcoming - Bulletin of Symbolic Logic:1-57.
    Hermann Weyl was one of the greatest mathematicians of the 20th century, with contributions to many branches of mathematics and physics. In 1918 he wrote a famous book, “Das Kontinuum”, on the foundations of mathematics. In that book he described mathematical analysis as a ‘house built on sand’, and tried to ‘replace this shifting foundation with pillars of enduring strength’. In this paper we reexamine and explain the philosophical and mathematical ideas that underly Weyl’s system in “Das Kontinuum”, and show (...)
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  19. Gödel’s Second Incompleteness Theorem: How It is Derived and What It Delivers.Saeed Salehi - forthcoming - Bulletin of Symbolic Logic:1-15.
    The proofs of G¨odel (1931), Rosser (1936), Kleene (first 1936 and second 1950), Chaitin (1970), and Boolos (1989) for the first incompleteness theorem are compared with each other, especially from the viewpoint of the second incompleteness theorem. It is shown that G¨odel’s (first incompleteness theorem) and Kleene’s first theorems are equivalent with the second incompleteness theorem, Rosser’s and Kleene’s second theorems do deliver the second incompleteness theorem, and Boolos’ theorem is derived from the second incompleteness theorem in the standard way. (...)
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  20. Proofs and Surfaces.Djordje Baralić, Pierre-Louis Curien, Marina Milićević, Jovana Obradović, Zoran Petrić, Mladen Zekić & Rade T. Živaljević - 2020 - Annals of Pure and Applied Logic 171 (9):102845.
    A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.
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  21. Pseudofinite Difference Fields and Counting Dimensions.Tingxiang Zou - forthcoming - Journal of Mathematical Logic:2050022.
    We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we also discuss the possible connection between coarse dimension and transformal transcendence degree in these difference fields.
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  22. Indicative Conditionals and Graded Information.Ivano Ciardelli - 2020 - Journal of Philosophical Logic 49 (3):509-549.
    I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of (...)
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  23. Realism and Empirical Equivalence.Eric Johannesson - 2020 - Journal of Philosophical Logic 49 (3):475-495.
    The main purpose of this paper is to investigate various notions of empirical equivalence in relation to the two main arguments for realism in the philosophy of science, namely the no-miracles argument and the indispensability argument. According to realism, one should believe in the existence of the theoretical entities postulated by empirically adequate theories. According to the no-miracles argument, one should do so because truth is the the best explanation of empirical adequacy. According to the indispensability argument, one should do (...)
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  24. A System of Axioms for Minkowski Spacetime.Lorenzo Cocco & Joshua Babic - 2020 - Journal of Philosophical Logic:1-37.
    We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...)
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  25. Replacing Truth?Matti Eklund - 2014 - In Brett Sherman & Alexis Burgess (eds.), Metasemantics.
  26. The Logic of Creativity.Carlos Blanco‐Pérez - 2020 - Heythrop Journal 61 (3):393-411.
  27. Ontology of Knowledge and the Form of the World 20200505.Jean-Louis Boucon - 2020 - Academia.
    In this article, we will try to illustrate how, according to the Ontology of Knowledge (OK), reality appears to the subject in the form of objects « in becoming » in a four-dimensional space whose time of the subject (his becoming) would be a privileged dimension. For the OK, reality is formless and it is the subject that gives it shape. The shape of the world results from the Logos, a transcendent principle by which the complexity of logical interdependence, the (...)
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  28. Expectation Biases and Context Management with Negative Polar Questions.Alex Silk - 2020 - Journal of Philosophical Logic 49 (1):51-92.
    This paper examines distinctive discourse properties of preposed negative 'yes/no' questions (NPQs), such as 'Isn’t Jane coming too?'. Unlike with other 'yes/no' questions, using an NPQ '∼p?' invariably conveys a bias toward a particular answer, where the polarity of the bias is opposite of the polarity of the question: using the negative question '∼p?' invariably expresses that the speaker previously expected the positive answer p to be correct. A prominent approach—what I call the context-management approach, developed most extensively by Romero (...)
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  29. From the Square to Octahedra.José David García Cruz - 2017 - In Jean-Yves Beziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Switzerland: pp. 253-272.
    Colwyn Williamson (Notre Dame J. Formal Log. 13:497–500, 1972) develops a comparison between propositional and syllogistic logic. He outlines an interpretation of the traditional square of opposition in terms of propositional logic, that is, the statements corresponding to the corners of the traditional square can be represented with propositional logic operators. His goal is to present a twofold square that preserves the truth conditions of the relationships between the formulas, and define other set of formulas that complete the traditional square (...)
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  30. Pure Logic and its Equivalence with the Universe: A Unique Method to Establish the Final Theory.Kai Jiang - 2019 - International Journal of Humanities and Social Sciences 9 (1):45-56.
    The theme of this study is about establishing a purely logical theory about the Universe. Logic is the premier candidate for the reality behind phenomena. If there is a final theory, the Universe must be logic itself, called pure logic, elements of which include not only logic and illogic but also logical and illogical manipulations between them. The kernel is the revised law of the excluded middle: between two basic concepts are four possible manipulations, three logical and one illogical, whereas (...)
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  31. Modelling Last-Act Attempted Crime in Criminal Law.Jiraporn Pooksook, Phan Minh Dung, Ken Satoh & Giovanni Sartor - 2019 - Journal of Applied Non-Classical Logics 29 (4):327-357.
    In the court of law, a person can be punished for attempting to commit a crime. An open issue in the study of Artificial Intelligence and Law is whether the law of attempts could be formally modelled. There are distinct legal rules for determining attempted crime whereas the last-act rule (also called proximity rule) represents the strictest approach. In this paper, we provide a formal model of the last-act rule using structured argumentation.
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  32. Categorical Equivalence Between $$\varvec{PMV}{\varvec{f}}$$ PMV f -Product Algebras and Semi-Low $$\varvec{f}{\varvec{u}}$$ f u -Rings.Lilian J. Cruz & Yuri A. Poveda - 2019 - Studia Logica 107 (6):1135-1158.
    An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean algebras are (...)
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  33. Algebraic Description of Limit Models in Classes of Abelian Groups.Marcos Mazari-Armida - 2020 - Annals of Pure and Applied Logic 171 (1):102723.
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  34. Coxeter Groups and Abstract Elementary Classes: The Right-Angled Case.Tapani Hyttinen & Gianluca Paolini - 2019 - Notre Dame Journal of Formal Logic 60 (4):707-731.
    We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes, for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results translates into (...)
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  35. On the Degree Structure of Equivalence Relations Under Computable Reducibility.Keng Meng Ng & Hongyuan Yu - 2019 - Notre Dame Journal of Formal Logic 60 (4):733-761.
    We study the degree structure of the ω-c.e., n-c.e., and Π10 equivalence relations under the computable many-one reducibility. In particular, we investigate for each of these classes of degrees the most basic questions about the structure of the partial order. We prove the existence of the greatest element for the ω-c.e. and n-computably enumerable equivalence relations. We provide computable enumerations of the degrees of ω-c.e., n-c.e., and Π10 equivalence relations. We prove that for all the degree classes considered, upward density (...)
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  36. The Marker–Steinhorn Theorem Via Definable Linear Orders.Erik Walsberg - 2019 - Notre Dame Journal of Formal Logic 60 (4):701-706.
    We give a short proof of the Marker–Steinhorn theorem for o-minimal expansions of ordered groups. The key tool is Ramakrishnan’s classification of definable linear orders in such structures.
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  37. Immobility Theory.Ninh Khac Son - manuscript
    The content of the manuscript represents a bold idea system, it is beyond the boundaries of all existing knowledge but the method of reasoning and logic is also very strict and scientific. The purpose of the manuscript is to unify the natural categories (natural philosophy, natural geometry, quantum mechanics, astronomy,…), and to open a new direction for most other sciences. Abstract of the manuscript: About Philosophy: • Proved the existence of time and non-dilation. • Proved that matter is always motionless (...)
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  38. The Logic of Conditional Belief.Benjamin Eva - forthcoming - Philosophical Quarterly.
    The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms -- the Lockean theory of belief and the Ramsey test for conditional belief -- are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker's semantics for the indicative did succeed in capturing (...)
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  39. Mathematical Rigor and Proof.Yacin Hamami - forthcoming - Review of Symbolic Logic:1-41.
    Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowl- edge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary (...)
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  40. De Zolt’s Postulate: An Abstract Approach.Eduardo N. Giovannini, Edward H. Haeusler, Abel Lassalle-Casanave & Paulo A. S. Veloso - forthcoming - Review of Symbolic Logic:1-28.
    A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons. We formulate an abstract version of this postulate and derive it from some selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5, and analyze its logical relation to the former proposition. These results prove (...)
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  41. The Modal Logic of Set-Theoretic Potentialism and the Potentialist Maximality Principles.Joel David Hamkins & Øystein Linnebo - forthcoming - Review of Symbolic Logic:1-36.
  42. Mereology with Super-Supplemention Axioms. A Reconstruction of the Unpublished Manuscript of Jan F. Drewnowski.Kordula Świętorzecka & Marcin Łyczak - forthcoming - Logic and Logical Philosophy:1.
    We present a study of unpublished fragments of Jan F. Drewnowski’s manuscript from the years 1922–1928, which contains his own axiomatics for mereology. The sources are transcribed and two versions of mereology are reconstructed from them. The first one is given by Drewnowski. The second comes from Leśniewski and was known to Drewnowski from Leśniewski’s lectures. Drewnowski’s version is expressed in the language of ontology enriched with the primitive concept of a (proper) part, and its key axiom expresses the so-called (...)
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  43. An Epistemic Approach to Nondeterminism: Believing in the Simplest Course of Events.James P. Delgrande & Hector J. Levesque - 2019 - Studia Logica 107 (5):859-886.
    This paper describes an approach for reasoning in a dynamic domain with nondeterministic actions in which an agent’s beliefs correspond to the simplest, or most plausible, course of events consistent with the agent’s observations and beliefs. The account is based on an epistemic extension of the situation calculus, a first-order theory of reasoning about action that accommodates sensing actions. In particular, the account is based on a qualitative theory of nondeterminism. Our position is that for commonsense reasoning, the world is (...)
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  44. Theory Choice, Theory Change, and Inductive Truth-Conduciveness.Konstantin Genin & Kevin T. Kelly - 2019 - Studia Logica 107 (5):949-989.
    Synchronic norms of theory choice, a traditional concern in scientific methodology, restrict the theories one can choose in light of given information. Diachronic norms of theory change, as studied in belief revision, restrict how one should change one’s current beliefs in light of new information. Learning norms concern how best to arrive at true beliefs. In this paper, we undertake to forge some rigorous logical relations between the three topics. Concerning, we explicate inductive truth conduciveness in terms of optimally direct (...)
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  45. Back to Basics: Belief Revision Through Direct Selection.Sven Hansson - 2019 - Studia Logica 107 (5):887-915.
    Traditionally, belief change is modelled as the construction of a belief set that satisfies a success condition. The success condition is usually that a specified sentence should be believed or not believed. Furthermore, most models of belief change employ a select-and-intersect strategy. This means that a selection is made among primary objects that satisfy the success condition, and the intersection of the selected objects is taken as outcome of the operation. However, the select-and-intersect method is difficult to justify, in particular (...)
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  46. Logique floue et arborescence comme outils de modélisation des catégories en tant que prototypes.Taraneh Javanbakht - 2016 - Dissertation, Université au Québec À Montréal
    The master's thesis of Dr. Taraneh Javanbakht in philosophy that was published at the Université du Québec à Montréal in 2016 includes her innovations in logic and cognitive sciences as well as some parts of her philosophical system, netism.
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  47. Decidability of the Theory of Modules Over Prüfer Domains with Dense Value Groups.Lorna Gregory, Sonia L'Innocente & Carlo Toffalori - 2019 - Annals of Pure and Applied Logic 170 (12):102719.
    We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.
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  48. Schmerl Decompositions in First Order Arithmetic.François Dorais, Zachary Evans, Marcia Groszek, Seth Harris & Theodore Slaman - 2019 - Annals of Pure and Applied Logic 170 (12):102717.
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  49. Reductions Between Types of Numberings.Ian Herbert, Sanjay Jain, Steffen Lempp, Manat Mustafa & Frank Stephan - 2019 - Annals of Pure and Applied Logic 170 (12):102716.
    This paper considers reductions between types of numberings; these reductions preserve the Rogers Semilattice of the numberings reduced and also preserve the number of minimal and positive degrees in their semilattice. It is shown how to use these reductions to simplify some constructions of specific semilattices. Furthermore, it is shown that for the basic types of numberings, one can reduce the left-r.e. numberings to the r.e. numberings and the k-r.e. numberings to the k+1-r.e. numberings; all further reductions are obtained by (...)
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  50. Supersimple Ω-Categorical Theories and Pregeometries.Vera Koponen - 2019 - Annals of Pure and Applied Logic 170 (12):102718.
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