How hard is it to compute a failure of the continuum hypothesis?

This is an invited talk at the Logic Across Mathematics section of the 2025 AWM Research Symposium on 17 May 2025

[Slides.]

Cohen discovered forcing to prove the consistency of the failure of the continuum hypothesis, and it has since become a central tool in set theory. This talk studies forcing from the perspective of computable structure theory to make precise and answer the titular question.

This talk is about joint work with Joel David Hamkins and Russell Miller.