Construction schemes: Finitizations of guessing principles and their parametrized forcing axioms.

Abstract: In this talk, we survey recent developments in the theory of capturing schemes introduced by Todorcevic. We present the capturing axioms CAρ​, CAΔ​, and CA, which may be viewed as finite-dimensional analogues of the classical guessing principles Club, CH, and Diamond, respectively. We show that many consequences traditionally derived from these guessing principles already follow from the capturing axioms, often with significantly simpler proofs. Finally, we introduce parametrized forcing axioms naturally associated with the capturing principles and demonstrate how they can be used to establish the independence of a strong statement about gaps over ω, a problem that cannot be settled using either traditional guessing principles or standard forcing axioms.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic