Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Undecidability of the Definability of Principal Subcongruences   For each Turing machine T, we construct an algebra A'(T) such that the
variety generated by A'(T) has definable principal subcongruences if and only
if T halts, thus proving that the property of having definable principal
subcongruences is undecidable for a finite algebra. A consequence of this is
that there is no algorithm that takes as input a finite algebra a decides
whether that algebra is finitely based.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
30
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: hep-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph