Date of Award

Spring 1-1-2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Keith Kearnes

Second Advisor

Agnes Szendrei

Third Advisor

Don Monk

Fourth Advisor

Markus Pflaum

Fifth Advisor

Ross Willard

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. Using this, we present another proof that A. Tarski's finite basis problem is undecidable.

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