Sharps and the Σ^1_3 correctness of K

Ralf Schindler

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arXiv · math/0201169

Sharps and the Σ^1_3 correctness of K

Ralf Schindler

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Abstract

Steel and Welch have shown that K is Σ^1_3 correct if the reals are closed under sharps but 0^\pistol doesn't exist. We'll give a simple and purely combinatorial proof of the following: K is Σ^1_3 correct if the reals are closed under sharps, there is no inner model with a Woodin cardinal, K exists, and * holds. Here, * is an assertion which can easily be verified if 0^\pistol doesn't exist. We conjecture that * holds outright. (* is denoted by \clubsuit in the paper.)

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BibTeX RIS

Ralf Schindler. 2002-01-18. Sharps and the Σ^1_3 correctness of K. https://arxiv.org/abs/math/0201169

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