CUNY Graduate Center
Virtual (email Victoria Gitman for meeting id)
Organized by Athar Abdul-Quader and Roman Kossak
Calendar
October 24
1:00pm NY time
Virtual (email Victoria Gitman for meeting id)
Alessandro Berarducci and Marcello Mamino
University of Pisa
TBA
Abstract
October 17
1:00pm NY time
Virtual (email Victoria Gitman for meeting id)
Elliot Glazer
Harvard University
Coin flipping on models of arithmetic to define the standard cut
Abstract
We will discuss the following claim: 'The standard cut of a model $M$ of PA (or even Q) is uniformly definable with respect to a randomly chosen predicate.' Restricting our consideration to countable models, this claim is true in the usual sense, i.e. there is a formula $\varphi$ such that for any countable model of arithmetic $M,$ the set $S_M^{\varphi} := \{P \subset M: \omega = \{x \in M: (M, P) \models \varphi(x)\} \}$ is Lebesgue measure 1. However, if $M$ is countably saturated, then there is no $\varphi$ such that $S_M^{\varphi}$ is measured by the completed product measure on $2^M.$ We will identify various combinatorial ideals on $2^M$ that can be used to formalize the original claim with no restriction on the cardinality of $M,$ and discuss the relationship between closure properties of these ideals and principles of choice.
Video
Previous Semesters