Developing Takeuti-Yasumoto forcing
Logic
2018-04-12 v1
Abstract
In late 90's G.Takeuti and Y.Yasumoto gave forcing constructions for bounded arithmetic. We will reformulate their constructions using two-sort bounded arithmetic and prove the followings. 1. Generic extensions are related with P=NP problem. 2. J.Krajicek's forcing constructions can be given as Takeuti-Yasumoto forcing. 3. We can either satisfy or falsify the dual weak pigeonhole principles in generic extensions.
Keywords
Cite
@article{arxiv.1804.03798,
title = {Developing Takeuti-Yasumoto forcing},
author = {Satoru Kuroda},
journal= {arXiv preprint arXiv:1804.03798},
year = {2018}
}
Comments
17 pages