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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Tarski’s finite basis problem via $\mathbf A(\mathcal T)$
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by Ross Willard PDF
Trans. Amer. Math. Soc. 349 (1997), 2755-2774 Request permission

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
  • Received by editor(s): October 18, 1995
  • Additional Notes: This research was supported by the NSERC of Canada
  • © Copyright 1997 American Mathematical Society
  • 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