Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forcing with matrices of countable elementary submodels   We analyze the forcing notion $\mathcal P$ of finite matrices whose rows
consists of isomorphic countable elementary submodels of a given structure of
the form $H_{\theta}$. We show that forcing with this poset adds a Kurepa tree
$T$. Moreover, if $\mathcal P_c$ is a suborder of $\mathcal P$ containing only
continuous matrices, then the Kurepa tree $T$ is almost Souslin, i.e. the level
set of any antichain in $T$ is not stationary in $\omega_1$.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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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: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph