Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-02T22:23:36.446Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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