Sur la complexité du principe de Tarski-Seidenberg
Sur la complexité du principe de Tarski-Seidenberg
Sur La Logique De Premier Ordre Et La Théorie Des Catégories.
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...
Sur les systèmes déductifs dans la logique -valente
Svenonius sentences and Lindström's theory on preservation theorems
Synthetic compontents of infinite classes of postulates.
Tame semiflows for piecewise linear vector fields
Let be a disjoint decomposition of and let be a vector field on , defined to be linear on each cell of the decomposition . Under some natural assumptions, we show how to associate a semiflow to and prove that such semiflow belongs to the o-minimal structure . In particular, when is a continuous vector field and is an invariant subset of , our result implies that if is non-spiralling then the Poincaré first return map associated is also in .
Tarski's problem about the elementary theory of free groups has a positive solution.
The alternation hierarchy for the theory of -lattices.
The Amalgamation Property, the Universal-Homogeneous Models, and the Generic Models.
The automorphism group of the random lattice is not amenable
We prove that the automorphism group of the random lattice is not amenable, and we identify the universal minimal flow for the automorphism group of the random distributive lattice.
The Axiom of Choice, the Löwenheim-Skolem Theorem and Borel models
The axiom of reflection
The contracted model of exploded real numbers.
The decidability of some -categorical theories
The degree spectra of definable relations on Boolean algebras.
The diameter of a Lascar strong type
We prove that a type-definable Lascar strong type has finite diameter. We also answer some other questions from [1] on Lascar strong types. We give some applications on subgroups of type-definable groups.
The dimension of hyperspaces of non-metrizable continua
We prove that, for any Hausdorff continuum X, if dim X ≥ 2 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then either dim C(X) = 2 or C(X) is not a C-space. This generalizes some results known for metric continua.
The directed geodetic structure of a strong digraph
By a ternary structure we mean an ordered pair , where is a finite nonempty set and is a ternary relation on . A ternary structure is called here a directed geodetic structure if there exists a strong digraph with the properties that and for all , where denotes the (directed) distance function in . It is proved in this paper that there exists no sentence of the language of the first-order logic such that a ternary structure is a directed geodetic structure if and only if it satisfies...