Developing Takeuti-Yasumoto forcing

Satoru Kuroda

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arXiv · 1804.03798

Developing Takeuti-Yasumoto forcing

Satoru Kuroda

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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.

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BibTeX RIS

Satoru Kuroda. 2018-04-11. Developing Takeuti-Yasumoto forcing. https://arxiv.org/abs/1804.03798

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