Logic Seminar

Jing Zhang, University of Toronto

"Compactness and incompactness in higher dimensional combinatorics"

We describe an organizing framework to study higher dimensional infinitary combinatorics based on \v{C}ech cohomology, originating from works by Barry Mitchell, Barbara Osofsky and others. A central combinatorial notion is $n$-dimensional coherence sequences, generalizing the 1-dimensional ones studied extensively by Todorcevic using the method of minimal walks. We will discuss ZFC results suggesting $\aleph_n$ is not "compact for $(n+1)$-dimensional combinatorics" and consistency results that any regular cardinal greater or equal to $\aleph_{\omega+1}$ can be "compact for $n$-dimensional combinatorics for all $n$". The talk will be purely combinatorial. Joint work with Jeffrey Bergfalk and Chris Lambie-Hanson.

MC 5479