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550
Quantifier Elimination over Finite Fields Using Gröbner Bases
, 2011
"... We give an algebraic quantifier elimination algorithm for the firstorder theory over any given finite field using Gröbner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algo ..."
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We give an algebraic quantifier elimination algorithm for the firstorder theory over any given finite field using Gröbner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity
PRIME QUANTIFIER ELIMINABLE RINGS
"... The main result of this paper is that a prime ring with a finite center which admits elimination of quantifiers must be finite. This answers a question raised by the author [10; p. 99] and completes the classification of prime rings which admit elimination of quantifiers. That is, a prime ring admit ..."
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admits elimination of quantifiers if and only if it is either an algebraically closed field, a finite field, or a 2 x 2 matrix ring over a finite prime field. Two features of this proof merit mentioning in this introduction. In [11] Rose and Woodrow developed the concept of ultrahomogeneity as distinct
Real Quantifier Elimination in the RegularChains Library
"... www.csd.uwo.ca/∼moreno Abstract. Quantifier elimination (QE) over real closed fields has found numerous applications. Cylindrical algebraic decomposition (CAD) is one of the main tools for handling quantifier elimination of nonlinear input formulas. Despite of its worst case doubly exponential compl ..."
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www.csd.uwo.ca/∼moreno Abstract. Quantifier elimination (QE) over real closed fields has found numerous applications. Cylindrical algebraic decomposition (CAD) is one of the main tools for handling quantifier elimination of nonlinear input formulas. Despite of its worst case doubly exponential
Understanding AlgebroGeometric Quantifier Elimination: Part I, Algebraically Closed Fields of Characteristic Zero via Muchnik
"... In this short expository note, we present a selfcontained proof that algebraically closed fields of characteristic zero admit elimination of quantifiers over the elementary language of rings. We do this by fleshing out a method due to Muchnik 1 (and possibly Cohen 2). This note is the first part of ..."
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In this short expository note, we present a selfcontained proof that algebraically closed fields of characteristic zero admit elimination of quantifiers over the elementary language of rings. We do this by fleshing out a method due to Muchnik 1 (and possibly Cohen 2). This note is the first part
Expressing cardinality quantifiers in monadic secondorder logic over chains
 J. Symb. Log
"... Abstract. We study an extension of monadic secondorder logic of order with the uncountability quantifier "there exist uncountably many sets". We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic secondorder logic of order. Addi ..."
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. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic secondorder logic over finitely branching trees, which is notable for not all of these classes are analytic. Our approach is based on Shelah's composition method and uses basic results from descriptive set
Relative Motives and the Theory of Pseudofinite Fields
"... We generalize the motivic incarnation morphism from the theory of arithmetic integration to the relative case, where we work over a base variety S over a field k of characteristic zero. We develop a theory of constructible effective Chow motives over S, and we show how to associate a motive to any ..."
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Cited by 8 (0 self)
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to any Svariety. We give a geometric proof of relative quantifier elimination for pseudofinite fields, and we construct a morphism from the Grothendieck ring of the theory of pseudofinite fields over S, to the tensor product of Q with the Grothendieck ring of constructible effective Chow motives
3 ON THE MAXIMUM ORDERS OF ELEMENTS OF FINITE ALMOST SIMPLE GROUPS AND PRIMITIVE PERMUTATION GROUPS
"... ar ..."
J. London Math. Soc. (2) 75 (2007) 545–562 C2007 London Mathematical Society doi:10.1112/jlms/jdm033 ON BASE SIZES FOR ACTIONS OF FINITE CLASSICAL GROUPS
"... Let G be a finite almost simple classical group and let Ω be a faithful primitive nonstandard Gset. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. Let b(G) be the minimal size of a base for G. A wellknown conjecture of Cameron and Kantor asserts that there exists an ab ..."
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an absolute constant c such that b(G) c for all such groups G, and the existence of such an undetermined constant has been established by Liebeck and Shalev. In this paper we prove that either b(G) 4, or G = U6(2) · 2, Gω = U4(3) · 22 and b(G) = 5. The proof is probabilistic, using bounds on fixed
Solving mixed quantified constraints over a domain based on real numbers and Herbrand terms
, 2001
"... Abstract. Combining the logic of hereditary Harrop formulas HH with a constraint system, a logic programming language is obtained that extends Horn clauses in two different directions, thus enhancing substantially the expressivity of Prolog. The implementation of this new language requires the abili ..."
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Cited by 2 (1 self)
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, based on elimination of quantifiers, one used for solving unification and disunification problems, the other used to solve polynomials. This combination provides a procedure to solve RHconstraints in the context of HH with constraints.
Results 1  10
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