Algebra Seminar talk
2026-04-17
Tristan van der Vlugt
Ideals on Higher Baire Spaces: Meagreness and Domination for Singular Cardinals
Abstract:
The higher Baire space is the family of functions ${}^\kappa\kappa$ for
$\kappa$ an uncountable cardinal. In most studies of the higher Baire
space, it is assumed that $\kappa$ is regular.
In this talk we will consider the alternative case where $\kappa$ is singular, as well as related spaces, such as ${}^{\rm{cf}(\kappa)}\kappa$. We will compare several reasonable (and unreasonable) topologies and the potential homeomorphisms between them. Our focus will be the $\rm{cf}(\kappa)$-meagre ideals (i.e. sets that are unions of $\rm{cf}(\kappa)$-many nowhere dense sets) and domination ideals in each of these respective topological spaces. We will also compare their associated cardinal invariants.
This is joint work with Yusuke Hayashi.