Séminaires : Séminaire Général de Logique

Equipe(s) : lm,
Responsables :S. Anscombe, A. Khélif, A. Vignati
Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr
Salle : 1013
Adresse :Sophie Germain

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Orateur(s) Francesco Parente - Université de Turin,
Titre Combinatorial properties of ultrafilters and their orderings on Boolean algebras
Horaire15:15 à 16:15
RésumeIn this talk, I shall report on joint work with Jörg Brendle, focusing on the combinatorial properties of ultrafilters on Boolean algebras in relation to the Tukey and Rudin-Keisler orderings. First, I aim to introduce the framework of Tukey reducibility and discuss the existence of non-maximal ultrafilters. Furthermore, I shall connect this discussion with a cardinal invariant of Boolean algebras, the ultrafilter number, and sketch consistency results (and open questions) concerning its possible values on Cohen and random algebras. Finally, I will analyse and compare two generalizations of the Rudin-Keisler ordering to ultrafilters on complete Boolean algebras, introducing new techniques to construct incomparable ultrafilters in this setting.
AdresseSophie Germain