Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on the ultrapower algebra of the hyperfinite factor   On page 43 in \cite{Po83} Sorin Popa asked whether the following property
holds: \emph{If $\omega$ is a free ultrafilter on $\mathbb N$ and $\mathcal
R_1\subseteq \mathcal R$ is an irreducible inclusion of hyperfinite II$_1$
factors such that $\mathcal R'\cap \mathcal R^\omega\subseteq \mathcal
R^\omega_1$ does it follows that $\mathcal R_1=\mathcal R$?} In this short note
we provide an affirmative answer to this question.

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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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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: quant-ph