Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-24T21:15:34.663Z Has data issue: false hasContentIssue false
  • English
  • Français

Decidable discriminator varieties from unary varieties

Published online by Cambridge University Press:  12 March 2014

Stanley Burris ,
Ralph Mckenzie  and
Matthew Valeriote
Stanley Burris
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 5S7, Canada
Ralph Mckenzie
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Matthew Valeriote
Affiliation:
Department of Mathematics and Statistics, Mcmaster University, Hamilton, Ontario L8S 4K1, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 4 , December 1991 , pp. 1355 - 1368
Copyright
Copyright © Association for Symbolic Logic 1991

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]Burris, S., Iterated discriminator varieties have undecidable theories, Algebra Universalis, vol. 21 (1985), pp. 54–61.CrossRefGoogle Scholar
[2]Burris, S. and McKenzie, R., Decidability and Boolean representations, Memoirs of the American Mathematical Society, vol. 246, American Mathematical Society, Providence, Rhode Island, 1981.Google Scholar
[3]Burris, S. and Sankappanavar, H. P., A course in universal algebra, Springer-Verlag, Berlin, 1981.CrossRefGoogle Scholar
[4]Burris, S. and Werner, H., Sheaf constructions and their elementary properties, Transactions of the American Mathematical Society, vol. 248 (1979), pp. 269–309.CrossRefGoogle Scholar
[5]Comer, S., Elementary properties of structures of sections, Boletin de la Sociedad Matemática Mexicana, vol. 19 (1974), pp. 78–85.Google Scholar
[6]Comer, S., Monadic algebras with finite degree, Algebra Universalis, vol. 5 (1975), pp. 315–327.CrossRefGoogle Scholar
[7]Ershov, Yu. L., Decidability of the elementary theory of relatively complemented distributive lattices and the theory of filters, Algebra i Logika, vol. 3 (1964), no. 3, pp. 17–38. (Russian)Google Scholar
[8]Ershov, Yu. L., On the elementary theory of Post varieties, Algebra i Logika, vol. 6 (1967), no. 5, pp. 7–15. (Russian)Google Scholar
[9]Hart, B. and Valeriote, M., A structure theorem for strongly abelian varieties with few models, this Journal, vol. 56 (1991), pp. 832–852.Google Scholar
[10]Hobby, D. and McKenzie, R., The structure of finite algebras, Contemporary Mathematics, vol. 76, American Mathematical Society, Providence, Rhode Island, 1988.CrossRefGoogle Scholar
[11]McKenzie, R., On spectra, and the negative solution of the decision problem for identities having a finite nontrivial model, this Journal, vol. 40 (1975), pp. 186–196.Google Scholar
[12]McKenzie, R., Decidability of the theory of the pure discriminator variety (notes by Burris, S.), University of California, Berkeley, California, 1976.Google Scholar
[13]McKenzie, R., Finite forbidden lattices, Universal algebra and lattice theory, Lecture Notes in Mathematics, vol. 1004, Springer-Verlag, Berlin, 1983, pp. 176–205.CrossRefGoogle Scholar
[14]McKenzie, R. and Valeriote, M., The structure of locally finite decidable varieties, Birkhäuser, Boston, Massachusetts, 1989.CrossRefGoogle Scholar
[15]Rubin, M., The theory of Boolean algebras with a distinguished sub-algebra is undecidable, Annales Scientifiques de l'Université de Clermont No. 60, Série Mathématique No. 13 (1976), pp. 129–134.Google Scholar
[16]Tarski, A., Arithmetical classes and types of Boolean algebras, Bulletin of the American Mathematical Society, vol. 55 (1949), p. 64.Google Scholar
[17]Valeriote, M., Decidable unary varieties, Algebra Universalis, vol. 24 (1987), pp. 1–20.CrossRefGoogle Scholar
[18]Valeriote, M. and Willard, R., Discriminating varieties, Algebra Universalis (to appear).Google Scholar
[19]Valeriote, Matthew, On decidable locally finite varieties, Ph.D. thesis, University of California, Berkeley, California, 1986.Google Scholar
[20]Willard, R., Decidable discriminator varieties from unary universal classes, Transactions of the American Mathematical Society (to appear).Google Scholar