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arXiv · 1301.5588

The Undecidability of the Definability of Principal Subcongruences

Matthew Moore
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Abstract

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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BibTeXRIS

Matthew Moore. 2013-01-22. The Undecidability of the Definability of Principal Subcongruences. https://doi.org/10.1017/jsl.2014.51

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