Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely separably MAD families and the modal logic of $\beta\omega$   We show in ZFC that the existence of completely separable maximal almost
disjoint families of subsets of $\omega$ implies that the modal logic S4.1.2 is
complete with respect to the \v{C}ech-Stone compactification of the natural
numbers, the space $\beta\omega$. In the same fashion we prove that the modal
logic S4 is complete with respect to the space
$\omega^*=\beta\omega\setminus\omega$. This improves the results of G.
Bezhanishvili and J. Harding who prove these theorems under stronger
assumptions ($\mathfrak{a}=\mathfrak{c}$). Our proof is also somewhat simpler.

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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci