Speaker: Brian Ransom
University of California - Irvine
Will give a Logic Seminar entitled:
On Ultrafilters in Symmetric Extensions
Abstract: In this talk, we describe several generalizations and adaptations of the speaker's proof of BPI in the generalized Cohen model. We first review this proof, which uses methods from Harrington's proof of the Halpern-Lauchli theorem, and is described in greater detail in the speaker's earlier talk at the Graduate Student Conference in Logic. From this argument, we observe two simple generalizations: a new proof that $ZF+BPI+DC_\kappa$ does not imply $AC$, and a preservation theorem for $BPI$ in products of generalized Cohen models. We then show how these methods can be adapted to describe ultrafilters in certain symmetric extensions in which $BPI$ fails, allowing us to answer questions posed in the literature.
Date: 04-29-2025
Time: 2:00 pm
Location: 125 Hayes-Healy Bldg