Exercices en stabilité
Exercices sur la stabilité
Exhaustive zero-convergence structures on Boolean algebras
Existence d'un contrôle optimal via l'analyse non standard.
In this article, we want to show that it is possible to give a complete theory about the existence of an optimal control, without introducing any functional space, by means of the Non Standard Analysis.
Existence of non measurable sets
Existence theorems for commutative diagrams.
Existency-Closed Groups in X_1 with Special Properties
Existential interpretation. II.
Existentially closed domains with radical relations.
Existentially closed II₁ factors
We examine the properties of existentially closed (-embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed (-embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().
Exotic logics
Expansions of models of ZFC.
Expansions of o-minimal structures by sparse sets
Given an o-minimal expansion ℜ of the ordered additive group of real numbers and E ⊆ ℝ, we consider the extent to which basic metric and topological properties of subsets of ℝ definable in the expansion (ℜ,E) are inherited by the subsets of ℝ definable in certain expansions of (ℜ,E). In particular, suppose that has no interior for each m ∈ ℕ and definable in ℜ, and that every subset of ℝ definable in (ℜ,E) has interior or is nowhere dense. Then every subset of ℝ definable in (ℜ,(S)) has interior...
Expansions of subfields of the real field by a discrete set
Let K be a subfield of the real field, D ⊆ K be a discrete set and f: Dⁿ → K be such that f(Dⁿ) is somewhere dense. Then (K,f) defines ℤ. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines ℤ. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.
Expansions of the real line by open sets: o-minimality and open cores
The open core of a structure ℜ := (ℝ,<,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core of ℜ is...
Expected values in the alternative set theory and their applications to some limit theorems
This article presents an alternative approach to statistical moments within non-standard models and by the help of these moments some limit theorems are reformulated and proved.
Exploded and compressed numbers.
Exploded and compressed spaces.
Exploring a Syntactic Notion of Modal Many-Valued Logics.
Exploring the gap between linear and classical logic.