Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Club Chang's Conjecture   Chang's Conjecture (CC) asserts that for every $F:[\omega_2]^{<\omega} \to
\omega_2$, there exists an $X$ that is closed under $F$ such that
$|X|=\omega_1$ and $|X \cap \omega_1| =\omega$. By classic results of Silver
and Donder, CC is equiconsistent with an $\omega_1$-Erdos cardinal. Using
stronger large cardinal assumptions (between $o(\kappa) = \kappa^+$ and
$o(\kappa) = \kappa^{++}$), we prove that it is consistent to also require that
$X$ contains a closed unbounded set of ordinals in $\text{sup}(X \cap
\omega_2)$. We denote this stronger principle \textbf{Club-CC}, and also show
that, unlike CC, Club-CC implies failure of certain weak square principles.

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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: bayes-an