Forcing as a Local Method of Accessing Small Extensions
Logic
2025-01-03 v2
Abstract
Fix a set-theoretic universe . We look at small extensions of as generalised degrees of computability over . We also formalise and investigate the complexity of certain methods one can use to define, in , subclasses of degrees over . Finally, we give a nice characterisation of the complexity of forcing within this framework.
Cite
@article{arxiv.2409.03441,
title = {Forcing as a Local Method of Accessing Small Extensions},
author = {Desmond Lau},
journal= {arXiv preprint arXiv:2409.03441},
year = {2025}
}
Comments
37 pages, 2 figures. Figure 2 is added to provide a better intuition of our main reducibility relation on local method definitions. Section 4 recapitulates some definitions and theorems from arXiv:2402.01213. Certain short proofs of these theorems are replicated for greater self-containment of the article