Le théorème d'ambiguïté et son extension à la logique intuitionniste

Doctorat en sciences mathématiques -- UCL, 199

Square-central elements in alternative algebras of characteristic 2

The Aim of this note is to investigate the class of alternative algebras of characteristic 2 in which the elements whose square is in the base field form a vector space which generates the algebra. Quatersion and octonion (or Cayley-) algebras are the main examples of such algebras, and our main result is indeed a characterization of these algebras

Fixed-points of set-continuous operators

In this paper, we study when a set-continuous operator has a fixed-point that is the intersection of a directed family. The framework of our study is the Kelley-Morse theory KMC- and the Gödel-Bernays theory GBC-, both theories including an Axiom of Choice and excluding the Axiom of Foundation. On the one hand, we prove a result concerning monotone operators in KMC- that cannot be proved in GBC-. On the other hand, we study conditions on directed superclasses in GBC- in order that their intersection is a fixed-point of a set-continuous operator. Finally, we illustrate our results with a solution to the liar paradox and a construction of maximal bisimulations.SCOPUS: ar.jFLWINinfo:eu-repo/semantics/publishe