Louise Hay Logic Seminar
Shehzad Ahmed
Ohio University
Jónsson Cardinals and Club Guessing
Abstract: We say that a cardinal $\lambda$ is a Jónsson cardinal if it satisfies the following weak Ramsey-type property: given any coloring
$F:[\lambda]^{<\omega} \rightarrow \lambda$ of the finite subsets of $\lambda$ in $\lambda$-many colors, there exists a set
$H \in [\lambda]^\lambda$ such that the range of $F \restriction [H]^{<\omega}$ is a proper subset of $\lambda$. One of the
big driving forces present in early chapters Cardinal Arithmetic is an attempt to understand the combinatorial structure at
and around Jónsson cardinals. The goal of this talk is to highlight the connection between Jónsson cardinals and various forms
of club guessing, which can be thought of as weakenings of $\diamond$ principles. Our focus will be on what happens at successors
of singulars, and I will attempt to explain why the following question is difficult: "Is it consistent that there exists a singular
cardinal $\mu$ such that $\mu^+$ is Jónsson?"
Thursday November 19, 2015 at 4:00 PM in SEO 427