Tarski’s finite basis problem via $\mathbf A(\mathcal T)$

Author:
Ross Willard

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2755-2774

MSC (1991):
Primary 03C05; Secondary 08B05

DOI:
https://doi.org/10.1090/S0002-9947-97-01807-2

MathSciNet review:
1389791

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Abstract | References | Similar Articles | Additional Information

Abstract: R. McKenzie has recently associated to each Turing machine $\mathcal {T}$ a finite algebra $\mathbf {A} (\mathcal {T})$ having some remarkable properties. We add to the list of properties, by proving that the equational theory of $\mathbf {A}(\mathcal {T})$ is finitely axiomatizable if $\mathcal {T}$ halts on the empty input. This completes an alternate (and simpler) proof of McKenzie’s negative answer to A. Tarski’s finite basis problem. It also removes the possibility, raised by McKenzie, of using $\mathbf {A}(\mathcal {T})$ to answer an old question of B. Jónsson.

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Additional Information

**Ross Willard**

Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Email:
rdwillar@flynn.uwaterloo.ca

Keywords:
Finite algebra,
equational theory,
finitely axiomatizable

Received by editor(s):
October 18, 1995

Additional Notes:
This research was supported by the NSERC of Canada

Article copyright:
© Copyright 1997
American Mathematical Society