Logic Seminar

Mark SchachnerCornell University
Whitehead's problem in the Cohen model

Monday, October 23, 2023 - 2:55pm
Malott 205

Continuing our investigation of Whitehead's problem in and out of the classical setting, we prove that if $A$ is a nonfree abelian group of size $\kappa$, then $A$ is not Whitehead in the extension of $V$ by the forcing $P$ adding $\kappa$-many Cohen reals. We show how this bridges the classical and condensed settings, since the Stone space of the boolean completion of $P$ plays an important role in the resolution of Whitehead's problem in condensed mathematics. All results due to Jeffrey Bergfalk, Chris Lambie-Hanson, and Jan Saroch.