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Quantifier Elimination
A test for eliminating quantifiers is given and applied it to further study the model theory of algebraically closed fields.
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A Proof of Bel’tyukov–Lipshitz Theorem by Quasi-Quantifier Elimination. II. The Main Reduction
AbstractThis paper is the second part of a new proof of the Bel’tyukov–Lipshitz theorem, which states that the existential theory of the structure
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Quantifier Elimination
In this chapter, we present several techniques for showing that a theory has quantifier elimination. We start by reducing the problem of quantifier...
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Connectivity of joins, cohomological quantifier elimination, and an algebraic Toda’s theorem
In this article, we use cohomological techniques to obtain an algebraic version of Toda’s theorem in complexity theory valid over algebraically...
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On Undecidability of Subset Theories of Some Unars
AbstractThis paper is dedicated to studying the algorithmic properties of unars with an injective function. We prove that the theory of every such...
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Cut elimination for coherent theories in negation normal form
We present a cut-free sequent calculus for a class of first-order theories in negation normal form which include coherent and co-coherent theories...
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Model Theory of the Real Field
We study the model theory of the real field, proving Tarski’s quantifier elimination and decidability results and studying its consequences. We...
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Glivenko sequent classes and constructive cut elimination in geometric logics
A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic and minimal infinitary logics with geometric...
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On algebraically closed fields with a distinguished subfield
This paper is concerned with the model-theoretic study of pairs ( K, F ) where K is an algebraically closed field and F is a distinguished subfield of K ...
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Vector spaces with a union of independent subspaces
We study the theory of K -vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite...
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Generalization of Shapiro’s theorem to higher arities and noninjective notations
In the framework of Stewart Shapiro, computations are performed directly on strings of symbols (numerals) whose abstract numerical interpretation is...
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Efficient elimination of Skolem functions in \(\text {LK}^\text {h}\)
We present a sequent calculus with the Henkin constants in the place of the free variables. By disposing of the eigenvariable condition, we obtained...
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Is Computer Algebra Ready for Conjecturing and Proving Geometric Inequalities in the Classroom?
We introduce an experimental version of GeoGebra that successfully conjectures and proves a large scale of geometric inequalities by providing an...
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Existential Definability of Unary Predicates in Büchi Arithmetic
The paper provides a complete characterisation of the sets $$S\subseteq \mathbb...
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Upper and Lower Bounds for the Height of Proofs in Sequent Calculus for Intuitionistic Logic
Upper and lower bounds for the height of proofs in sequent calculus for intuitionistic logic are proved for the case when cut formulas may only...
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The Lattice of Definability: Origins, Recent Developments, and Further Directions
AbstractThis article presents results and open problems related to definability spaces (reducts) and sources of this field since the 19th century....
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Divisible Rigid Groups. III. Homogeneity and Quantifier Elimination
A group G is said to be rigid if it contains a normal series G = G 1 > G 2 > . . . > G m > G m +1 = 1, whose quotients G i / G i +1 are Abelian and, treated as...
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Algebraically Closed Fields
We establish a simple algebraic elimination of quantifiers procedure for the theory of algebraically closed fields. This theory is model complete...