Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Ultrapower Axiom   The inner model problem for supercompact cardinals, one of the central open
problems in modern set theory, asks whether there is a canonical model of set
theory with a supercompact cardinal. The problem is closely related to the more
precise question of the equiconsistency of strongly compact cardinals and
supercompact cardinals. This dissertation approaches these two problems
abstractly by introducing a principle called the Ultrapower Axiom which is
expected to hold in all known canonical models of set theory. By investigating
the consequences of the Ultrapower Axiom under the hypothesis that there is a
supercompact cardinal, we provide evidence that the inner model problem can be
solved. Moreover, we establish that under the Ultrapower Axiom, strong
compactness and supercompactness are essentially equivalent.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: quant-ph