This is an talk at the Connectict Logic Seminar on 12 November 2024.

[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. It has enjoyed ample study from many perspectives. This talk is about a small piece of this larger project, investigating forcing from the perspective of computability. Using ideas from computable structure theory we can make precise the titular question. Akin to Hegel’s dialectical method, we will first see that the answer is no, then see that the answer is yes, and finally come to a synthesis of these two answers.

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