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6142 found
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1 — 50 / 6142
  1. added 2020-06-03
    Pseudofinite H-Structures and Groups Definable in Supersimple H-Structures.Tingxiang Zou - 2019 - Journal of Symbolic Logic 84 (3):937-956.
    In this article we explore some properties of H-structures which are introduced in [2]. We describe a construction of H-structures based on one-dimensional asymptotic classes which preserves pseudofiniteness. That is, the H-structures we construct are ultraproducts of finite structures. We also prove that under the assumption that the base theory is supersimple of SU-rank one, there are no new definable groups in H-structures. This improves the corresponding result in [2].
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  2. added 2020-06-03
    Weak Saturation and Weak Amalgamation Property.Ivan di Liberti - 2019 - Journal of Symbolic Logic 84 (3):929-936.
    We study the two model-theoretic concepts of weak saturation and weak amalgamation property in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly saturated objects of an accessible category ${\cal K}$. We discuss the implications of this fact in classical model theory.
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  3. added 2020-06-03
    On the Number of Countable Models of a Countable Nsop1 Theory Without Weight Ω.Byunghan Kim - 2019 - Journal of Symbolic Logic 84 (3):1168-1175.
    In this article, we prove that if a countable non-${\aleph _0}$-categorical NSOP1 theory with nonforking existence has finitely many countable models, then there is a finite tuple whose own preweight is ω. This result is an extension of a theorem of the author on any supersimple theory.
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  4. added 2020-06-03
    An Abstract Elementary Class Nonaxiomatizable In.Simon Henry - 2019 - Journal of Symbolic Logic 84 (3):1240-1251.
    We show that for any uncountable cardinal λ, the category of sets of cardinality at least λ and monomorphisms between them cannot appear as the category of points of a topos, in particular is not the category of models of a ${L_{\infty,\omega }}$-theory. More generally we show that for any regular cardinal $\kappa < \lambda$ it is neither the category of κ-points of a κ-topos, in particular, nor the category of models of a ${L_{\infty,\kappa }}$-theory.The proof relies on the construction (...)
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  5. added 2020-06-03
    Countable Models of the Theories of Baldwin–Shi Hypergraphs and Their Regular Types.Danul K. Gunatilleka - 2019 - Journal of Symbolic Logic 84 (3):1007-1019.
    We continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ (...)
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  6. added 2020-05-26
    Weakly Minimal Groups with a New Predicate.Gabriel Conant & Michael C. Laskowski - forthcoming - Journal of Mathematical Logic.
    Fix a weakly minimal (i.e. superstable U-rank 1) structure M. Let M∗ be an expansion by constants for an elementary substructure, and let A be an arbitrary subset of the universe M. We show that all formulas in the expansion (M∗,A) are equivalent to bounded formulas, and so (M,A) is stable (or NIP) if and only if the M-induced structure AM on A is stable (or NIP). We then restrict to the case that M is a pure abelian group with (...)
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  7. added 2020-05-26
    Model Theory of Steiner Triple Systems.Silvia Barbina & Enrique Casanovas - forthcoming - Journal of Mathematical Logic:2050010.
    A Steiner triple system (STS) is a set S together with a collection B of subsets of S of size 3 such that any two elements of S belong to exactly one element of B. It is well known that the class of finite STS has a Fraïssé limit M_F. Here, we show that the theory T of M_F is the model completion of the theory of STSs. We also prove that T is not small and it has quantifier elimination, (...)
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  8. added 2020-05-26
    Determinate Logic and the Axiom of Choice.J. P. Aguilera - 2020 - Annals of Pure and Applied Logic 171 (2):102745.
    Takeuti introduced an infinitary proof system for determinate logic and showed that for transitive models of Zermelo-Fraenkel set theory with the Axiom of Dependent Choice that contain all reals, the cut-elimination theorem is equivalent to the Axiom of Determinacy, and in particular contradicts the Axiom of Choice. We consider variants of Takeuti's theorem without assuming the failure of the Axiom of Choice. For instance, we show that if one removes atomic formulae of infinite arity from the language of Takeuti's proof (...)
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  9. added 2020-05-26
    Uniformly Locally o-Minimal Structures and Locally o-Minimal Structures Admitting Local Definable Cell Decomposition.Masato Fujita - 2020 - Annals of Pure and Applied Logic 171 (2):102756.
    We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which (...)
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  10. added 2020-05-26
    Model Theory and Machine Learning.Hunter Chase & James Freitag - 2019 - Bulletin of Symbolic Logic 25 (3):319-332.
    About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory and machine learning. The following years saw a fruitful exchange of ideas between PAC-learning and the model theory of NIP structures. In this article, we point out a new and similar connection between model theory and machine learning, this time developing a correspondence between stability and learnability in various settings of online learning. In particular, this gives many new (...)
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  11. added 2020-05-25
    First-Order Possibility Models and Finitary Completeness Proofs.Matthew Harrison-Trainor - 2019 - Review of Symbolic Logic 12 (4):637-662.
    This article builds on Humberstone’s idea of defining models of propositional modal logic where total possible worlds are replaced by partial possibilities. We follow a suggestion of Humberstone by introducing possibility models for quantified modal logic. We show that a simple quantified modal logic is sound and complete for our semantics. Although Holliday showed that for many propositional modal logics, it is possible to give a completeness proof using a canonical model construction where every possibility consists of finitely many formulas, (...)
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  12. added 2020-05-25
    The Fundamental Theorem of World Theory.Edward N. Zalta & Christopher Menzel - 2014 - Journal of Philosophical Logic 43 (2-3):333-363.
    The fundamental principle of the theory of possible worlds is that a proposition p is possible if and only if there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possible worlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this general theory has very small (...)
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  13. added 2020-05-20
    Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability.Frederik Van De Putte & Dominik Klein - forthcoming - Studia Logica:1-47.
    We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein. The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction”, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique’s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.
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  14. added 2020-05-20
    Extender-Based Forcings with Overlapping Extenders and Negations of the Shelah Weak Hypothesis.Moti Gitik - forthcoming - Journal of Mathematical Logic.
    Extender-based Prikry–Magidor forcing for overlapping extenders is introduced. As an application, models with strong forms of negations of the Shelah Weak Hypothesis for various cofinalities are constructed.
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  15. added 2020-05-20
    Definable Operators on Stable Set Lattices.Robert Goldblatt - forthcoming - Studia Logica:1-18.
    A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have a relational semantics provided by structures based on polarities. Such structures have associated complete lattices of stable subsets, and these have been used to construct canonical extensions of lattice-based algebras. We study classes of structures that are closed under ultraproducts and whose (...)
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  16. added 2020-05-20
    A Canonical Model for Constant Domain Basic First-Order Logic.Ben Middleton - forthcoming - Studia Logica:1-17.
    I build a canonical model for constant domain basic first-order logic (BQLCD), the constant domain first-order extension of Visser’s basic propositional logic, and use the canonical model to verify that BQLCD satisfies the disjunction and existence properties.
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  17. added 2020-05-19
    Epimorphisms, Definability and Cardinalities.T. Moraschini, J. G. Raftery & J. J. Wannenburg - 2020 - Studia Logica 108 (2):255-275.
    We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures. This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most \ non-logical symbols and an axiomatization requiring at most \ variables, if the epimorphisms into structures with at most \ elements are surjective, then so are all of the epimorphisms. Using these facts, we formulate and prove manageable ‘bridge theorems’, matching the surjectivity of all epimorphisms in (...)
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  18. added 2020-05-19
    The Tree Property at First and Double Successors of Singular Cardinals with an Arbitrary Gap.Alejandro Poveda - 2020 - Annals of Pure and Applied Logic 171 (5):102778.
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  19. added 2020-05-19
    Extended Contact Algebras and Internal Connectedness.Tatyana Ivanova - 2020 - Studia Logica 108 (2):239-254.
    The notion of contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with an additional relation C, called contact. Standard models of contact algebras are topological and are the contact algebras of regular closed sets in a given topological space. In such a contact algebra we add the predicate of internal connectedness with the following meaning—a regular closed set is internally connected if and only if its interior is (...)
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  20. added 2020-05-19
    Diagonal Supercompact Radin Forcing.Omer Ben-Neria, Chris Lambie-Hanson & Spencer Unger - 2020 - Annals of Pure and Applied Logic 171 (10):102828.
    Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular $k>\aleph_1$, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.
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  21. added 2020-05-19
    Infinite Forcing and the Generic Multiverse.Giorgio Venturi - 2020 - Studia Logica 108 (2):277-290.
    In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.
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  22. added 2020-05-19
    Countably Many Weakenings of Belnap–Dunn Logic.Minghui Ma & Yuanlei Lin - 2020 - Studia Logica 108 (2):163-198.
    Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...)
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  23. added 2020-05-16
    Intuitionistic Non-normal Modal Logics: A General Framework.Tiziano Dalmonte, Charles Grellois & Nicola Olivetti - forthcoming - Journal of Philosophical Logic:1-50.
    We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a Hilbert (...)
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  24. added 2020-05-16
    Univalent polymorphism.Benno van den Berg - 2020 - Annals of Pure and Applied Logic 171 (6):102793.
    We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category EFF. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as such provide a context in which one can interpret many notions from homotopy theory and Homotopy Type Theory. Within the path category EFF one can identify a class of discrete fibrations which is closed under push forward along arbitrary fibrations (in other words, this (...)
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  25. added 2020-05-15
    A Premouse Inheriting Strong Cardinals From V.Farmer Schlutzenberg - 2020 - Annals of Pure and Applied Logic 171 (9):102826.
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  26. added 2020-05-15
    Epimorphism Surjectivity in Varieties of Heyting Algebras.T. Moraschini & J. J. Wannenburg - 2020 - Annals of Pure and Applied Logic 171 (9):102824.
    It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K . It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that (...)
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  27. added 2020-05-15
    Perfect Tree Forcings for Singular Cardinals.Natasha Dobrinen, Dan Hathaway & Karel Prikry - 2020 - Annals of Pure and Applied Logic 171 (9):102827.
  28. added 2020-05-15
    2008 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '08.Alex J. Wilkie - 2009 - Bulletin of Symbolic Logic 15 (1):95-139.
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  29. added 2020-05-12
    Indestructibility of the Tree Property.Radek Honzik & Šárka Stejskalová - 2020 - Journal of Symbolic Logic 85 (1):467-485.
    In the first part of the article, we show that if $\omega \le \kappa < \lambda$ are cardinals, ${\kappa ^{ < \kappa }} = \kappa$, and λ is weakly compact, then in $V\left[M {\left} \right]$ the tree property at $$\lambda = \left^{V\left[ {\left} \right]} $$ is indestructible under all ${\kappa ^ + }$-cc forcing notions which live in $V\left[ {{\rm{Add}}\left} \right]$, where ${\rm{Add}}\left$ is the Cohen forcing for adding λ-many subsets of κ and $\left$ is the standard Mitchell forcing for (...)
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  30. added 2020-05-12
    Silver Type Theorems for Collapses.Moti Gitik - 2020 - Annals of Pure and Applied Logic 171 (9):102825.
    Let κ be a cardinal of cofinality \omega_1 witnessed by a club of cardinals (κ_\alpha | \alpha < \omega_1) . We study Silver's type effects of collapsing of κ^+_\alphas 's on κ^+ . A model in which κ^+_\alphas 's (and also κ^+) are collapsed on a stationary co-stationary set is constructed.
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  31. added 2020-05-11
    Kripke Semantics for Intuitionistic Łukasiewicz Logic.A. Lewis-Smith, P. Oliva & E. Robinson - forthcoming - Studia Logica:1-27.
    This paper proposes a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Łukasiewicz logic IŁL — a logic in the intersection between IL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009) to show the decidability (and PSPACE completeness) of the quasiequational theory of commutative, integral and bounded GBL algebras. The main idea is that w \Vdash \sigma—which for IL is (...)
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  32. added 2020-05-11
    Distality for the Asymptotic Couple of the Field of Logarithmic Transseries.Allen Gehret & Elliot Kaplan - 2020 - Notre Dame Journal of Formal Logic 61 (2):341-361.
    We show that the theory Tlog of the asymptotic couple of the field of logarithmic transseries is distal. As distal theories are NIP, this provides a new proof that Tlog is NIP.
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  33. added 2020-05-11
    Uniformly Bounded Arrays and Mutually Algebraic Structures.Michael C. Laskowski & Caroline A. Terry - 2020 - Notre Dame Journal of Formal Logic 61 (2):265-282.
    We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure M. We prove that if T is a complete L-theory, then T is mutually algebraic if and only if there is some model M of T for which every atomic formula has uniformly bounded arrays. Moreover, an incomplete theory T is mutually algebraic if and only if every atomic formula has uniformly bounded arrays in every model M of T.
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  34. added 2020-05-11
    On Morita Equivalence and Interpretability.Paul Anh Mceldowney - 2020 - Review of Symbolic Logic 13 (2):388-415.
    In a recent article, Barrett & Halvorson define a notion of equivalence for first-order theories, which they call “Morita equivalence.” To argue that Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of the claim that Morita extensions “say no more” than the theories they are extending. The goal of this article is to challenge this central claim by raising objections to their argument for it and by showing why there is good reason to think that the (...)
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  35. added 2020-05-11
    Varieties of de Morgan Monoids: Covers of Atoms.T. Moraschini, J. G. Raftery & J. J. Wannenburg - 2020 - Review of Symbolic Logic 13 (2):338-374.
    The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...)
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  36. added 2020-05-06
    Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic.Norihiro Kamide & Yoni Zohar - 2020 - Studia Logica 108 (3):549-571.
    In this study, we prove the completeness and cut-elimination theorems for a first-order extension F4CC of Arieli, Avron, and Zamansky’s ideal paraconsistent four-valued logic known as 4CC. These theorems are proved using Schütte’s method, which can simultaneously prove completeness and cut-elimination.
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  37. added 2020-05-06
    Simplified Kripke-Style Semantics for Some Normal Modal Logics.Andrzej Pietruszczak, Mateusz Klonowski & Yaroslav Petrukhin - 2020 - Studia Logica 108 (3):451-476.
    Pietruszczak :163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics \, \ ), \ are determined by suitable classes of simplified Kripke frames of the form \, where \. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of \. Furthermore, a modal logic is a normal extension of \ ; \; \) if and only if it is (...)
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  38. added 2020-05-06
    Recursive Functions and Existentially Closed Structures.Emil Jeřábek - 2019 - Journal of Mathematical Logic 20 (1):2050002.
    The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...)
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  39. added 2020-02-12
    Descriptive Complexity.Steven Lindell - 2001 - Bulletin of Symbolic Logic 7 (4):525-527.
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  40. added 2020-02-12
    Fine Structure and Class Forcing.M. C. Stanley - 2001 - Bulletin of Symbolic Logic 7 (4):522-525.
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  41. added 2020-02-12
    Α-Decompositions of Α-Spaces.Northrup Fowler Iii - 1976 - Journal of Symbolic Logic 41 (2):483-488.
  42. added 2020-02-11
    Analytic Quotients.D. Fremlin - 2006 - Bulletin of Symbolic Logic 12 (1):126-128.
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  43. added 2020-02-11
    The Essential Turing.Jan Obdržálek - 2005 - Bulletin of Symbolic Logic 11 (4):541-542.
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  44. added 2020-02-11
    Being No One: The Self-Model Theory of Subjectivity.George Graham - 2004 - Mind 113 (450):369-372.
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  45. added 2020-02-11
    Topics in Topology.Ilijas Farah - 2002 - Bulletin of Symbolic Logic 8 (4):526-528.
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  46. added 2020-02-11
    Handbook of Recursive Mathematics, Volume 1, Recursive Model Theory.Bakhadyr Khoussainov - 2001 - Bulletin of Symbolic Logic 7 (1):66-69.
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  47. added 2020-02-11
    Handbook of Recursive Mathematics, Volume 2, Recursive Algebra, Analysis and Combinatorics.John N. Crossley - 2001 - Bulletin of Symbolic Logic 7 (1):69-71.
  48. added 2020-02-11
    Combinatorial Series and Recursive Equivalence Types.A. B. Manaster - 1968 - Journal of Symbolic Logic 33 (4):620-621.
  49. added 2020-02-08
    Computable Calculus.Douglas Bridges - 2002 - Bulletin of Symbolic Logic 8 (3):426-428.
  50. added 2019-12-12
    Forma y Modalidad. Una Introducción al Concepto de Consecuencia Lógica.Mario Gomez-Torrente - 2000 - Buenos Aires, CABA, Argentina: Eudeba.
1 — 50 / 6142