Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong meager properties for filters   We analyze several ``strong meager'' properties for filters on the natural
numbers between the classical Baire property and a filter being $F_\sigma$. Two
such properties have been studied by Talagrand and a few more combinatorial
ones are investigated. In particular, we define the notion of a P$^+$-filter, a
generalization of the traditional concept of P-filter, and prove the existence
of a non-meager P$^+$-filter. Our motivation lies in understanding the
structure of filters generated by complements of members of a maximal almost
disjoint family.

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The categories of this paper are: funct-an
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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: atom-ph
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
18
The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con