Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knaster and friends I: Closed colorings and precalibers   The productivity of the $\kappa$-chain condition, where $\kappa$ is a
regular, uncountable cardinal, has been the focus of a great deal of
set-theoretic research. In the 1970s, consistent examples of $\kappa$-cc posets
whose squares are not $\kappa$-cc were constructed by Laver, Galvin, Roitman
and Fleissner. Later, $\mathsf{ZFC}$ examples were constructed by Todorcevic,
Shelah, and others. The most difficult case, that in which $\kappa = \aleph_2$,
was resolved by Shelah in 1997.
  In this work, we obtain analogous results regarding the infinite productivity
of strong chain conditions, such as the Knaster property. Among other results,
for any successor cardinal $\kappa$, we produce a $\mathsf{ZFC}$ example of a
poset with precaliber $\kappa$ whose $\omega^{\mathrm{th}}$ power is not
$\kappa$-cc. To do so, we carry out a systematic study of colorings satisfying
a strong unboundedness condition. We prove a number of results indicating
circumstances under which such colorings exist, in particular focusing on cases
in which these colorings are moreover closed.

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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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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: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con