Covering versus partitioning with Polish spaces

03.11.2022 15:00 - 16:30

W. Brian (U of North Carolina at Charlotte, US)

A topological space is Polish if it is second countable and completely metrizable. We may think of these as the small, or "essentially countable" members of the category of completely metrizable spaces. In this talk, we explore the question of whether, given a completely metrizable space \(X\), it is possible to cover \(X\) with fewer Polish spaces than it can be partitioned into. Surprisingly, this question not only turns out to be independent of ZFC, but proving its independence requires large cardinal axioms. I will sketch some of the ideas that go into one direction of this independence proof. Specifically, I will describe how a version of the model-theoretic transfer principle called Chang's Conjecture implies that there is a completely metrizable space that can be covered with fewer Polish spaces than it can be partitioned into.

Students at Uni Wien are required to attend in person.

Organiser:

KGRC

Location:

SR 10, 1. Stock, Koling. 14-16, 1090 Wien

SR 10, 1. Stock, Koling. 14-16, 1090 Wien