This will be talk for the CUNY Set Theory seminar, Friday, March 22, 2019, 10 am in room 6417 at the CUNY Graduate Center.

Abstract. I shall discuss recent joint work with Victoria Gitman and Asaf Karagila, in which we proved that Kelley-Morse set theory (which includes the global choice principle) does not prove the class Fodor principle, the assertion that every regressive class function 𝐹 :𝑆 →Ord defined on a stationary class 𝑆 is constant on a stationary subclass. Indeed, it is relatively consistent with KM for any infinite 𝜆 with 𝜔 ≤𝜆 ≤Ord that there is a class function 𝐹 :Ord →𝜆 that is not constant on any stationary class. Strikingly, it is consistent with KM that there is a sequence of classes 𝐴𝑛, each containing a class club, but the intersection of all 𝐴𝑛 is empty. Consequently, it is relatively consistent with KM that the class club filter is not 𝜎-closed.

I am given to understand that the talk will be streamed live online. I’ll post further details when I have them.