Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharps and the \Sigma^1_3 correctness of K   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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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph