Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariants Related to the Tree Property   We consider global analogues of model-theoretic tree properties. The main
objects of study are the invariants related to Shelah's tree property
$\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, and
$\kappa_{\text{inp}}(T)$ and the relations that obtain between them. From
strong colorings, we construct theories $T$ with $\kappa_{\text{cdt}}(T) >
\kappa_{\text{sct}}(T) + \kappa_{\text{inp}}(T)$. We show that these invariants
have distinct structural consequences, by investigating the decay of saturation
in ultrapowers of models of $T$, where $T$ is some theory with
$\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, or $\kappa_{\text{inp}}(T)$
large and bounded. This answers some questions of Shelah.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci