Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Selectively (a)-spaces from almost disjoint families are necessarily
  countable under a certain parametrized weak diamond principle   The second author has recently shown ([20]) that any selectively (a) almost
disjoint family must have cardinality strictly less than $2^{\alpeh_0}$, so
under the Continuum Hypothesis such a family is necessarily countable. However,
it is also shown in the same paper that $2^{\alpeh_0} < 2^{\alpeh_1}$ alone
does not avoid the existence of uncountable selectively (a) almost disjoint
families. We show in this paper that a certain effective parametrized weak
diamond principle is enough to ensure countability of the almost disjoint
family in this context. We also discuss the deductive strength of this specific
weak diamond principle (which is consistent with the negation of the Continuum
Hypothesis, apart from other features).

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The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex