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Steven Givant [21]Steven R. Givant [2]
  1.  40
    A Formalization of Set Theory Without Variables.Alfred Tarski & Steven R. Givant - 1987 - American Mathematical Soc..
    Completed in 1983, this work culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. Written in collaboration with Steven Givant, the book appeals to a very broad audience, and requires only a familiarity with first-order logic. It is of great interest to logicians and mathematicians interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, algebraic logic, or the methodology of the deductive sciences, and to (...)
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  2. Tarski's System of Geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.
    This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski's system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of the system suitable for the development of 1-dimensional geometry.
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  3. Logic as Algebra.Paul Halmos & Steven Givant - 1998 - American Mathematical Soc..
    Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and (...)
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  4.  9
    Nonrepresentable Relation Algebras From Groups.Hajnal Andréka, István Németi & Steven Givant - 2020 - Review of Symbolic Logic 13 (4):861-881.
    A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We present our main construction in terms of polygroupoids.
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  5.  60
    Bibliography of Alfred Tarski.Steven Givant - 1986 - Journal of Symbolic Logic 51 (4):913-941.
  6. Introduction to Boolean Algebras. Undergraduate Texts in Mathematics.Steven Givant & Paul Halmos - 2010 - Bulletin of Symbolic Logic 16 (2):281-282.
  7.  24
    Notions of Density That Imply Representability in Algebraic Logic.Hajnal Andréka, Steven Givant, Szabolcs Mikulás, István Németi & András Simon - 1998 - Annals of Pure and Applied Logic 91 (2-3):93-190.
    Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...)
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  8.  15
    Universal Horn Classes Categorical or Free in Power.Steven Givant - 1978 - Annals of Mathematical Logic 15 (1):1-53.
  9.  5
    Nonrepresentable Relation Algebras From Groups - Addendum.Hajnal Andréka, István Németi & Steven Givant - 2019 - Review of Symbolic Logic 12 (4):892-892.
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  10.  16
    A Representation Theorem for Measurable Relation Algebras.Steven Givant & Hajnal Andréka - 2018 - Annals of Pure and Applied Logic 169 (11):1117-1189.
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  11.  10
    The Variety of Coset Relation Algebras.Steven Givant & Hajnal Andréka - 2018 - Journal of Symbolic Logic 83 (4):1595-1609.
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  12.  23
    Groups and Algebras of Binary Relations.Steven Givant & Hajnal Andréka - 2002 - Bulletin of Symbolic Logic 8 (1):38-64.
    In 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras, He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jonsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even if one (...)
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  13.  35
    The Lattice of Varieties of Representable Relation Algebras.Hajnal Andréka, Steven Givant & István Németi - 1994 - Journal of Symbolic Logic 59 (2):631-661.
    We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.
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  14.  15
    On Tarski’s Axiomatic Foundations of the Calculus of Relations.Hajnal Andréka, Steven Givant, Peter Jipsen & István Németi - 2017 - Journal of Symbolic Logic 82 (3):966-994.
    It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, (...)
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  15.  27
    Perfect Extensions and Derived Algebras.Hajnal Andréka, Steven Givant & István Németi - 1995 - Journal of Symbolic Logic 60 (3):775-796.
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  16.  5
    A Representation Theorem for Universal Horn Classes Categorical in Power.Steven Givant - 1979 - Annals of Mathematical Logic 17 (1-2):91-116.
  17.  29
    Inequivalent Representations of Geometric Relation Algebras.Steven Givant - 2003 - Journal of Symbolic Logic 68 (1):267-310.
    It is shown that the automorphism group of a relation algebra ${\cal B}_P$ constructed from a projective geometry P is isomorphic to the collineation group of P. Also, the base automorphism group of a representation of ${\cal B}_P$ over an affine geometry D is isomorphic to the quotient of the collineation group of D by the dilatation subgroup. Consequently, the total number of inequivalent representations of ${\cal B}_P$ , for finite geometries P, is the sum of the numbers ${\mid Col(P)\mid\over (...)
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  18.  1
    Decision Problems for Equational Theories of Relation Algebras.H. Andréka, Steven R. Givant & I. Németi - 1997 - American Mathematical Soc..
    This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the (...)
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  19.  23
    Universal Classes of Simple Relation Algebras.Steven Givant - 1999 - Journal of Symbolic Logic 64 (2):575-589.
  20.  4
    Universal Theories Categorical in Power and Κ-Generated Models.Steven Givant & Saharon Shelah - 1994 - Annals of Pure and Applied Logic 69 (1):27-51.
    We investigate a notion called uniqueness in power κ that is akin to categoricity in power κ, but is based on the cardinality of the generating sets of models instead of on the cardinality of their universes. The notion is quite useful for formulating categoricity-like questions regarding powers below the cardinality of a theory. We prove, for universal theories T, that if T is κ-unique for one uncountable κ, then it is κ-unique for every uncountable κ; in particular, it is (...)
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