On indecomposable ultrafilters at every successor of singular, part 1

Seminar
Speaker
Inbar Oren (HUJI)
Date
08/02/2024 - 16:00 - 14:00Add to Calendar 2024-02-08 14:00:00 2024-02-08 16:00:00 On indecomposable ultrafilters at every successor of singular, part 1 Indecomposability of an ultrafilter is a weakening of a completeness of an ultrafilter. Ben-David and Magidor showed that it is possible to obtain an indecomposable ultrafilter at א_{ω+1}. In our work, we extend their result to obtain indecomposable ultrafilters at every successor of a singular cardinal. This result will be the focus of our talks. We will also provide applications in two separate directions. Firstly, we will apply one of Shelah’s results to obtain a model where the compactness of chromatic numbers of graphs holds on every successor of a singular. We will also apply a proof from Raghavan and Shelah to show that for any fixed successor of a singular, it is consistent to have a small ultrafilter number at that cardinal. Secondly, we will give a few examples where Silver type theorems fail. This is joint work with Sittinon Jirattikansakul and Assaf Rinot Seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Seminar room
Abstract

Indecomposability of an ultrafilter is a weakening of a completeness of an ultrafilter. Ben-David and Magidor showed that it is possible to obtain an indecomposable ultrafilter at א_{ω+1}. In our work, we extend their result to obtain indecomposable ultrafilters at every successor of a singular cardinal. This result will be the focus of our talks.
We will also provide applications in two separate directions. Firstly, we will apply one of Shelah’s results to obtain a model where the compactness of chromatic numbers of graphs holds on every successor of a singular. We will also apply a proof from Raghavan and Shelah to show that for any fixed successor of a singular, it is consistent to have a small ultrafilter number at that cardinal. Secondly, we will give a few examples where Silver type theorems fail.

This is joint work with Sittinon Jirattikansakul and Assaf Rinot

Last Updated Date : 31/01/2024