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Steven Givant [12]Steven R. Givant [2]
  1. Steven Givant & Paul Halmos (2010). Introduction to Boolean Algebras. Undergraduate Texts in Mathematics. Bulletin of Symbolic Logic 16 (2):281-282.
     
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  2. Steven Givant (2003). Inequivalent Representations of Geometric Relation Algebras. 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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  3. Steven Givant & Hajnal Andreka (2002). Groups and Algebras of Binary Relations. 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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  4. Steven Givant (1999). Universal Classes of Simple Relation Algebras. Journal of Symbolic Logic 64 (2):575-589.
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  5. Alfred Tarski & Steven Givant (1999). Tarski's System of Geometry. 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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  6. Hajnal Andréka, Steven Givant, Szabolcs Mikulás, István Németi & András Simon (1998). Notions of Density That Imply Representability in Algebraic Logic. 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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  7. Paul R. Halmos & Steven R. Givant (1998). Logic as Algebra. Monograph Collection (Matt - Pseudo).
     
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  8. Hajnal Andréka, Steven Givant & István Németi (1995). Perfect Extensions and Derived Algebras. Journal of Symbolic Logic 60 (3):775-796.
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  9. Hajnal Andréka, Steven Givant & István Németi (1994). The Lattice of Varieties of Representable Relation Algebras. 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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  10. Steven Givant & Saharon Shelah (1994). Universal Theories Categorical in Power and Κ-Generated Models. 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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  11. Alfred Tarski & Steven R. Givant (1987). A Formalization of Set Theory Without Variables. Monograph Collection (Matt - Pseudo).
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  12. Steven Givant (1986). Bibliography of Alfred Tarski. Journal of Symbolic Logic 51 (4):913-941.
  13. Steven Givant (1979). A Representation Theorem for Universal Horn Classes Categorical in Power. Annals of Mathematical Logic 17 (1-2):91-116.
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  14. Steven Givant (1978). Universal Horn Classes Categorical or Free in Power. Annals of Mathematical Logic 15 (1):1-53.
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