Tue, March 24, 2026
1:50 pm - 3:00 pm
Dulles Hall 027
Brian Ransom
UC Irvine
Title
Compactness without choice
Abstract
One can quickly get the sense that the compactness theorem for first-order logic cannot be applied (over ZF alone) to wellorder an arbitrary set. Despite this correct intuition, there have been relatively few proofs of the compactness theorem in models without choice, and the difficulty of these proofs is remarked upon in the literature. In this talk, we present a new framework to prove compactness in models without choice. We will then use this framework to give simpler new proofs of several classical independence results.