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  1. The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
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  • Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
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  • Cylindric Algebras. Part I.Leon Henkin, J. Donald Monk, Alfred Tarski, L. Henkin, J. D. Monk & A. Tarski - 1985 - Journal of Symbolic Logic 50 (1):234-237.
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  • Finite axiomatizability using additional predicates.W. Craig & R. L. Vaught - 1958 - Journal of Symbolic Logic 23 (3):289-308.
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  • Cylindric Algebras. Part II.Leon Henkin, J. Donald Monk & Alfred Tarski - 1988 - Journal of Symbolic Logic 53 (2):651-653.
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  • Algebraic Logic.Paul Richard Halmos - 2014 - New York, NY, USA: Chelsea.
    2014 Reprint of 1962 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. In "Algebraic Logic" Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra. This book addresses some of the problems of mathematical logic and the theory of polyadic Boolean algebras in particular. It is intended to be an efficient (...)
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  • Nonfinitizability of classes of representable cylindric algebras.J. Donald Monk - 1969 - Journal of Symbolic Logic 34 (3):331-343.
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  • (1 other version)The lattice of modal logics: An algebraic investigation.W. J. Blok - 1980 - Journal of Symbolic Logic 45 (2):221-236.
    Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...)
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  • Quantifiers as modal operators.Steven T. Kuhn - 1980 - Studia Logica 39 (2-3):145 - 158.
    Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.
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  • Nonfinite axiomatizability results for cylindric and relation algebras.Roger D. Maddux - 1989 - Journal of Symbolic Logic 54 (3):951-974.
    The set of equations which use only one variable and hold in all representable relation algebras cannot be derived from any finite set of equations true in all representable relation algebras. Similar results hold for cylindric algebras and for logic with finitely many variables. The main tools are a construction of nonrepresentable one-generated relation algebras, a method for obtaining cylindric algebras from relation algebras, and the use of relation algebras in defining algebraic semantics for first-order logic.
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  • Modal definability in enriched languages.Valentin Goranko - 1989 - Notre Dame Journal of Formal Logic 31 (1):81-105.
    The paper deals with polymodal languages combined with standard semantics defined by means of some conditions on the frames. So, a notion of "polymodal base" arises which provides various enrichments of the classical modal language. One of these enrichments, viz. the base £(R,-R), with modalities over a relation and over its complement, is the paper's main paradigm. The modal definability (in the spirit of van Benthem's correspondence theory) of arbitrary and ~-elementary classes of frames in this base and in some (...)
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  • Abstract.[author unknown] - 1998 - Studies in History and Philosophy of Science Part A 29 (2):299-303.
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  • Interpolation properties of superintuitionistic logics.Larisa L. Maksimova - 1979 - Studia Logica 38 (4):419 - 428.
    A family of prepositional logics is considered to be intermediate between the intuitionistic and classical ones. The generalized interpolation property is defined and proved is the following.Theorem on interpolation. For every intermediate logic L the following statements are equivalent:(i) Craig's interpolation theorem holds in L, (ii) L possesses the generalized interpolation property, (iii) Robinson's consistency statement is true in L.
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  • Nonfinitizability of classes of representable polyadic algebras.James S. Johnson - 1969 - Journal of Symbolic Logic 34 (3):344-352.
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  • The Craig interpolation theorem for prepositional logics with strong negation.Valentin Goranko - 1985 - Studia Logica 44 (3):291 - 317.
    This paper deals with, prepositional calculi with strong negation (N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them.
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  • A sequent calculus for relation algebras.Roger Maddux - 1983 - Annals of Pure and Applied Logic 25 (1):73-101.
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  • An axiomatization of predicate functor logic.Steven T. Kuhn - 1983 - Notre Dame Journal of Formal Logic 24 (2):233-241.
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  • Non-finite-axiomatizability results in algebraic logic.Balázs Biró - 1992 - Journal of Symbolic Logic 57 (3):832 - 843.
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  • (1 other version)On universal algebraic constructions of logics.H. Andréka, T. Gergely & I. Németi - 1977 - Studia Logica 36 (1-2):9 - 47.
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  • Predicate functors revisited.W. V. Quine - 1981 - Journal of Symbolic Logic 46 (3):649-652.
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  • Local definability theory.Gonzalo E. Reyes - 1970 - Annals of Mathematical Logic 1 (1):95-137.
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  • (1 other version)Finitary Algebraic Logic.Roger D. Maddux - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (4):321-332.
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  • (1 other version)Finitary Algebraic Logic.Roger D. Maddux - 1989 - Mathematical Logic Quarterly 35 (4):321-332.
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  • (1 other version)A first approach to abstract modal logics.Josep M. Font & Ventura Verdú - 1989 - Journal of Symbolic Logic 54 (3):1042-1062.
    The object of this paper is to make a study of four systems of modal logic (S4, S5, and their intuitionistic analogues IM4 and IM5) with the techniques of the theory of abstract logics set up by Suszko, Bloom, Brown, Verdú and others. The abstract concepts corresponding to such systems are defined as generalizations of the logics naturally associated to their algebraic models (topological Boolean or Heyting algebras, general or semisimple). By considering new suitably defined connectives and by distinguishing between (...)
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  • (1 other version)Über eine natürliche Erweiterung des Relationenkalkuls.Paul Bernays - 1959 - In A. Heyting (ed.), Constructivity in mathematics. Amsterdam,: North-Holland Pub. Co.. pp. 1--14.
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  • On varieties of cylindric algebras with applications to logic.I. Németi - 1987 - Annals of Pure and Applied Logic 36:235-277.
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  • 2.W. V. Quine - 1968 - In W. V. O. Quine (ed.), Ontological relativity. New York,Columbia University Press. pp. 26--68.
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  • Self-Reference and Modal Logic.[author unknown] - 1987 - Studia Logica 46 (4):395-398.
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  • The completeness of a predicate-functor logic.John Bacon - 1985 - Journal of Symbolic Logic 50 (4):903-926.
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  • An algebraic study of well-foundedness.Robert Goldblatt - 1985 - Studia Logica 44 (4):423 - 437.
    A foundational algebra ( , f, ) consists of a hemimorphism f on a Boolean algebra with a greatest solution to the condition f(x). The quasi-variety of foundational algebras has a decidable equational theory, and generates the same variety as the complex algebras of structures (X, R), where f is given by R-images and is the non-wellfounded part of binary relation R.The corresponding results hold for algebras satisfying =0, with respect to complex algebras of wellfounded binary relations. These algebras, however, (...)
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  • Peirce, frege, the logic of relations, and church's theorem.Randall R. Dipert - 1984 - History and Philosophy of Logic 5 (1):49-66.
    In this essay, I discuss some observations by Peirce which suggest he had some idea of the substantive metalogical differences between logics which permit both quantifiers and relations, and those which do not. Peirce thus seems to have had arguments?which even De Morgan and Frege lacked?that show the superior expressiveness of relational logics.
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  • (1 other version)Isomorphic but not lower base-isomorphic cylindric set algebras.B. Biró & S. Shelah - 1988 - Journal of Symbolic Logic 53 (3):846-853.
    This paper belongs to cylindric-algebraic model theory understood in the sense of algebraic logic. We show the existence of isomorphic but not lower base-isomorphic cylindric set algebras. These algebras are regular and locally finite. This solves a problem raised in [N 83] which was implicitly present also in [HMTAN 81]. This result implies that a theorem of Vaught for prime models of countable languages does not continue to hold for languages of any greater power.
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  • Axiomatizing logics closely related to varieties.W. Rautenberg - 1991 - Studia Logica 50 (3-4):607 - 622.
    Let V be a s.f.b. (strongly finitely based, see below) variety of algebras. The central result is Theorem 2 saying that the logic defined by all matrices (A, d) with d A V is finitely based iff the A V have 1st order definable cosets for their congruences. Theorem 3 states a similar axiomatization criterion for the logic determined by all matrices (A, A), A V, a term which is constant in V. Applications are given in a series of examples.
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  • Universal Algebra.P. M. Cohn - 1969 - Journal of Symbolic Logic 34 (1):113-114.
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  • Cylindric algebras with terms.Norman Feldman - 1990 - Journal of Symbolic Logic 55 (2):854-866.
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  • Axiom systems for first order logic with finitely many variables.James S. Johnson - 1973 - Journal of Symbolic Logic 38 (4):576-578.
    J. D. Monk has shown that for first order languages with finitely many variables there is no finite set of schema which axiomatizes the universally valid formulas. There are such finite sets of schema which axiomatize the formulas valid in all structures of some fixed finite size.
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  • Topological duality for diagonalizable algebras.Claudio Bernardi & Paola D'Aquino - 1988 - Notre Dame Journal of Formal Logic 29 (3):345-364.
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  • (1 other version)Algebraic Analysis of the Topological Logic L(I).George Georgescu - 1982 - Mathematical Logic Quarterly 28 (27‐32):447-454.
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  • (1 other version)Algebraic Analysis of the Topological Logic L.George Georgescu - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (27-32):447-454.
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  • (1 other version)Toward a calculus of concepts.W. V. Quine - 1936 - Journal of Symbolic Logic 1 (1):2-25.
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  • R⌝-algebras and r⌝-model structures as power constructs.Chris Brink - 1989 - Studia Logica 48 (1):85 - 109.
    In relevance logic it has become commonplace to associate with each logic both an algebraic counterpart and a relational counterpart. The former comes from the Lindenbaum construction; the latter, called a model structure, is designed for semantical purposes. Knowing that they are related through the logic, we may enquire after the algebraic relationship between the algebra and the model structure. This paper offers a complete solution for the relevance logic R. Namely, R-algebras and R-model structures can be obtained from each (...)
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  • A simple algebra of first order logic.Charles C. Pinter - 1973 - Notre Dame Journal of Formal Logic 14 (3):361-366.
    A new system of algebraic logic is described. it is closely related to cylindric and polyadic algebras, and is axiomatized by a small number of very simple equations.
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  • Topological representations of post algebras of order ω+ and open theories based on ω+-valued post logic.Helena Rasiowa - 1985 - Studia Logica 44 (4):353 - 368.
    Post algebras of order + as a semantic foundation for +-valued predicate calculi were examined in [5]. In this paper Post spaces of order + being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order + are defined. A representation theorem for Post algebras of order + as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a given set (...)
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  • Copeland algebras.Daniel B. Demaree - 1972 - Journal of Symbolic Logic 37 (4):646-656.
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  • Algebraic logic with generalized quantifiers.Charles C. Pinter - 1975 - Notre Dame Journal of Formal Logic 16 (4):511-516.
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  • (1 other version)Algebraic Semantics for Modal Predicate Logic.James B. Freeman - 1976 - Mathematical Logic Quarterly 22 (1):523-552.
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  • (1 other version)Algebraic Semantics for Modal Predicate Logic.James B. Freeman - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):523-552.
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  • Near-equational and equational systems of logic for partial functions. I.William Craig - 1989 - Journal of Symbolic Logic 54 (3):795-827.
    Equational logic for total functions is a remarkable fragment of first-order logic. Rich enough to lend itself to many uses, it is also quite austere. The only predicate symbol is one for a notion of equality, and there are no logical connectives. Proof theory for equational logic therefore is different from proof theory for other logics and, in some respects, more transparent. The question therefore arises to what extent a logic with a similar proof theory can be constructed when expressive (...)
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  • Dynamic logic with program specifications and its relational proof system.Ewa Orlowska - 1993 - Journal of Applied Non-Classical Logics 3 (2):147-171.
    ABSTRACT Propositional dynamic logic with converse and test, is enriched with complement, intersection and relational operations of weakest prespecification and weakest postspecification. Relational deduction system for the logic is given based on its interpretation in the relational calculus. Relational interpretation of the operators ?repeat? and ?loop? is given.
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  • Q-ultrafilters and normal ultrafilters in b-algebras.Bronis?aw Tembrowski - 1986 - Studia Logica 45 (2):167 - 179.
    The first part of the paper deals with some subclasses of B-algebras and their applications to the semantics of SCI B , the Boolean strengthening of the sentential calculus with identity (SCI). In the second part a generalization of the McKinsey-Tarski construction of well-connected topological Boolean, algebras to the class of B-algebras is given.
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