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THE UNDECIDABILITY OF THE DEFINABILITY OF PRINCIPAL SUBCONGRUENCES

  • MATTHEW MOORE (a1)

Abstract

For each Turing machine ${\cal T}$ , we construct an algebra $\mathbb{A}$ $\left( {\cal T} \right)$ such that the variety generated by $\mathbb{A}$ $\left( {\cal T} \right)$ has definable principal subcongruences if and only if ${\cal T}$ 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 and decides whether that algebra is finitely based.

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Keywords

THE UNDECIDABILITY OF THE DEFINABILITY OF PRINCIPAL SUBCONGRUENCES

  • MATTHEW MOORE (a1)

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