Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of measures after adding a real   We prove that if $\mathcal{A}$ is an infinite Boolean algebra in the ground
model $V$ and $\mathbb{P}$ is a notion of forcing adding any of the following
reals: a Cohen real, an unsplit real, or a random real, then, in any
$\mathbb{P}$-generic extension $V[G]$, $\mathcal{A}$ has neither the Nikodym
property nor the Grothendieck property. A similar result is also proved for a
dominating real and the Nikodym property.

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The categories of this paper are: patt-sol
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: cs