Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thin ultrafilters, P-hierarchu and MArtin Axiom   Under MA we prove that for the ideal $\cal I$ of thin sets on $\omega$ and
for any ordinal $\gamma \leq \omega_1$ there is an ${\cal I}$-ultrafilter (in
the sense of Baumgartner), which belongs to the class ${\cal P}_{\gamma}$ of
P-hierarchy of ultrafilters. Since the class of ${\cal P}_2$ ultrafilters
coincides with a class of P-points, out result generalize theorem of
Fla\v{s}kov\'a, which states that there are ${\cal I}$-ultrafilters which are
not P-points. It is also related to theorem which states that under CH for any
tall P-ideal $\cal I$ on $\omega$ there is an ${\cal I}$-ultrafilter, however
the ideal of thin sets is not P-ideal.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: astro-ph