Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Tree Properties for Small Cardinals   An inaccessible cardinal kappa is supercompact when (kappa, lambda)-ITP holds
for all lambda greater than or equal to kappa. We prove that if there is a
model of ZFC with infinitely many supercompact cardinals, then there is a model
of ZFC where for every natural number n greater than 1 and for every ordinal mu
greater than or equal to aleph_n, we have (aleph_n, mu)-ITP.

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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: hep-ex