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Recursive inseparability for residual bounds of finite algebras

Published online by Cambridge University Press:  12 March 2014

Ralph McKenzie
Ralph McKenzie*
Affiliation:
Vanderbilt University, Department of Mathematics, 1326 Stevenson Center, Nashville, TN 37240, USA, E-mail:[email protected]
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Abstract

We exhibit a construction which produces for every Turing machine T with two halting states μ0 and μ−1, an algebra B(T) (finite and of finite type) with the property that the variety generated by B(T) is residually large if T halts in state μ−1, while if T halts in state μ0 then this variety is residually bounded by a finite cardinal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1863 - 1880
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[1]Latting, C., There is no algorithm to decide whether the residual character of a finite algebra is uncountable, Ph.D. dissertation, UC Berkeley, 1995.Google Scholar
[2]McKenzie, R., The residual bounds of finite algebras, International Journal of Algebra and Computation, vol. 6 (1996), pp. 1–28.CrossRefGoogle Scholar
[3]McKenzie, R., The residual bound of a finite algebra is not computable, International Journal of Algebra and Computation, vol. 6 (1996), pp. 29–48.CrossRefGoogle Scholar
[4]McKenzie, R., Tarski's finite basis problem is undecidable, International Journal of Algebra and Computation, vol. 6 (1996), pp. 49–104.CrossRefGoogle Scholar
[5]McKenzie, R. and Shelah, S., The cardinals of simple models for universal theories, Proceedings of the Tarski Symposium, Symposia in Pure Mathematics, vol. 25. American Mathematical Society, 1974, pp. 53–74.Google Scholar
[6]McKenzie, R. and Wood, J., The type-set of a variety is not computable, International Journal of Algebra and Computation, to appear.Google Scholar
[7]Quackenbush, R. W., Equational classes generated by finite algebras, Algebra Universalis, vol. 1 (1971), pp. 265–266.CrossRefGoogle Scholar
[8]Taylor, W., Residually small varieties, Algebra Universalis, vol. 2 (1972), pp. 33–53.CrossRefGoogle Scholar
[9]Willard, R., On McKenzie's method, Periodica Mathematica Hungarica, vol. 32 (1996), pp. 149–165.CrossRefGoogle Scholar
[10]Willard, R., Tarski's finite basis problem via A(T), Transactions of the American Mathematical Society, vol. 349 (1997), pp. 2755–2774.CrossRefGoogle Scholar
[11]Willard, R., Three lectures on the RS problem, Algebraic model theory (Hart, B. T.et al., editors), Kluwer Academic Publishers, 1997, pp. 231–254.CrossRefGoogle Scholar
[12]Willard, R., A finite basis theorem for residually finite, congruence meet-semidistributive varieties, this Journal, to appear.Google Scholar
[13]Willard, R., Determining whether V(A) has a model companion is undecidable, manuscript.Google Scholar