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ModelTheoretic Methods in Combined Constraint Satisfiability
 Journal of Automated Reasoning
, 2004
"... We extend NelsonOppen combination procedure to the case of theories which are compatible with respect to a common subtheory in the shared signature. The notion of compatibility relies on model completions and related concepts from classical model theory. ..."
Abstract

Cited by 40 (10 self)
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We extend NelsonOppen combination procedure to the case of theories which are compatible with respect to a common subtheory in the shared signature. The notion of compatibility relies on model completions and related concepts from classical model theory.
Axiomatisability of Weakly Flat, Flat and Projective SActs
 Comm. Alg. 2002
, 2000
"... . This paper gives necessary and sufficient conditions on a monoid S such that the class of flat left Sacts is (first order) axiomatisable. It presents also a streamlined version of the result of Stepanova that the class of projective left Sacts is axiomatisable if and only if the strongly flat le ..."
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Cited by 4 (3 self)
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. This paper gives necessary and sufficient conditions on a monoid S such that the class of flat left Sacts is (first order) axiomatisable. It presents also a streamlined version of the result of Stepanova that the class of projective left Sacts is axiomatisable if and only if the strongly flat left Sacts are axiomatisable and S is left perfect. 1.
The Context.................................. The Satisfiability Problem........................
, 2008
"... THÈSE présentée et soutenue publiquement le date pour l’obtention du Doctorat de l’université Henri Poincaré – Nancy 1 Composition du jury Président: (spécialité informatique) ..."
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THÈSE présentée et soutenue publiquement le date pour l’obtention du Doctorat de l’université Henri Poincaré – Nancy 1 Composition du jury Président: (spécialité informatique)
STABILITY OF THE THEORY OF EXISTENTIALLY CLOSED SACTS OVER A RIGHT COHERENT MONOID S
"... For Professor L.A. Bokut on the occasion of his 70th birthday Abstract. Let LS denote the language of (right) Sacts over a monoid S and let ΣS be a set of sentences in LS which axiomatises Sacts. A general result of model theory says that ΣS has a model companion, denoted by TS, precisely when the ..."
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For Professor L.A. Bokut on the occasion of his 70th birthday Abstract. Let LS denote the language of (right) Sacts over a monoid S and let ΣS be a set of sentences in LS which axiomatises Sacts. A general result of model theory says that ΣS has a model companion, denoted by TS, precisely when the class E of existentially closed Sacts is axiomatisable and in this case, TS axiomatises E. It is known that TS exists if and only if S is right coherent. Moreover, by a result of Ivanov, TS has the modeltheoretic property of being stable. In the study of stable first order theories, superstable and totally transcendental theories are of particular interest. These concepts depend upon the notion of type: we describe types over TS algebraically, thus reducing our examination of TS to consideration of the lattice of right congruences of S. We indicate how to use our result to confirm that TS is stable and to prove another result of Ivanov, namely that TS is superstable if and only if S satisfies the maximal condition for right ideals. The situation for total transcendence is more complicated but again we can use our description of types to ascertain for which right coherent monoids S we have that TS is totally transcendental and is such that the Urank of any type coincides with its Morley rank. 1.