Safety- and liveness-properties in propositional temporal logic: characterizations and decidability
Sentences with three quantifiers are decidable in set theory
Sheaf constructions in universal algebra and model theory
Solving word equations
Some decidable congruences of free monoids
Let be the free monoid over a finite alphabet . We prove that a congruence of generated by a finite number of pairs , where and , is always decidable.
Some decidable theories with finitely many covers which are decidable and algorithmically found
In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable...
Some remarks on well-ordered models
Some simple decidability proofs
Some undecidable theories with monadic predicates and without equality.
Statistical deducibility testing with stochastic parameters
Sur la théorie élémentaire des groupes libres
Sela a annoncé une solution complète d’un problème de Tarski, qui demanda vers 1945 quels sont les groupes de type fini qui ont la même théorie élémentaire qu’un groupe libre. Nous discuterons des travaux de Remeslennikov, Kharlampovich-Myasnikov, Sela, Champetier-Guirardel et autres sur la structure des groupes limites (les groupes de type fini qui sont “limites”de groupes libres, ou encore, qui ont la même théorie universelle qu’un groupe libre). Nous indiquerons quelques outils utilisés par Sela...