Sharps and the Σ^1_3 correctness of K

Details Sharps and the Σ^1_3 correctness of K Sharps and the Σ^1_3 correctness of K

2002-01-18

arxiv.org/abs/math/0201169v1

Mathematics

Logic

5 pages

Scientific paper

Steel and Welch have shown that K is \Sigma^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 \Sigma^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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