Thesis Defense
Will Adkisson
UIC
Infinitary Combinatorics Near Singular Cardinals
Abstract: I will discuss several different results, all loosely motivated by examining the behavior of combinatorial properties at or near singular cardinals. In particular, I will discuss the longstanding problem of obtaining the tree property (an uncountable generalization of König's Lemma) and its strengthenings at many successive cardinals. I will also discuss mutual stationarity, a property that gives an analogue for stationary sets at singular cardinals, and show that it can be combined with the tree property and with the failure of SCH.
If you wish to attend remotely, please contact me for the zoom link.
Friday March 15, 2024 at 4:30 PM in 636 SEO