Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Varieties generated by completions   We prove that persistently finite algebras are not created by completions of
algebras, in any ordered discriminator variety. A persistently finite algebra
is one without infinite simple extensions. We prove that finite measurable
relation algebras are all persistently finite. An application of these theorems
is that the variety generated by the completions of representable relation
algebras does not contain all relation algebras. This answers Problem 1.1(1)
from a paper by R. Maddux in the negative. At the same time, we confirm the
suggestion in that paper that the finite maximal relation algebras constructed
in a joint paper by M. Frias and R. Maddux are not in the variety generated by
the completions of representable relation algebras. We prove that there are
continuum many varieties between the variety generated by the completions of
representable relation algebras and the variety of relation algebras.

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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex