Canonical notions of forcing in computability theory

Abstract: In reverse mathematics, a proof that a problem P does not imply a problem Q is usually done by constructing a computable instance of Q whose solutions are computationally complex, while proving that every simple instance of P has a simple solution, using a notion of forcing. In its full generality, the notion of forcing could depend on both P and Q, but in most cases, the notion of forcing for building solutions to P does not depend on Q. This suggests the existence of a "canonical" notion of forcing for P, that is, a notion of forcing such that all the relevant separation proofs can be obtained without loss of generality with sufficiently generic sets for this notion. We settle a formal framework for discussing this question, and give preliminary results. This is a joint work with Denis Hirschfeldt.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic