Skip to main content
Log in

The decision problem for finite algebras from arithmetical varieties with equationally definable principal congruences

  • Published:
algebra universalis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. W. J. Blok, P. Köhler andD. Pigozzi,On the structure of varieties with equationally definable principal congruences II, Algebra Universalis,18 (1984), 334–379.

    Google Scholar 

  2. W. J. Blok andD. Pigozzi,On the structure of varieties with equationally definable principal congruences I, Algebra Universalis,15 (1982), 195–227.

    Google Scholar 

  3. S.Burris and R.McKenzie,Decidability and Boolean Representation, Mem. Amer. Math. Soc.246 (1981).

  4. S. Burris andH. P. Sankappanavar,Lattice-theoretic decision problems in universal algebra, Algebra Universalis,5 (1975), 163–177.

    Google Scholar 

  5. S.Burris and H. P.Sankappanavar,A Course in Universal Algebra, Springer Verlag 1981.

  6. S. D. Comer,Elementary properties of structure of sections, Bol. Soc. Mat. Mexicana,19 (1976), 183–190.

    Google Scholar 

  7. K. Idziak,Undecidability of Brouwerian semilattices, Algebra Universalis,22 (1986), 298–301.

    Google Scholar 

  8. K.Idziak and P. M.Idziak,Decidability problem for finite Heyting algebras, to appear in Journal of Symbolic Logic,53 (1988).

  9. P. M. Idziak,Undecidability of free pseudocomplemented distributive lattices, Reports on Mathematical Logic,21 (1987), 97–100.

    Google Scholar 

  10. P. M. Idziak,Undecidability of free pseudocomplemented semilattices, Publ. RIMS Kyoto Univ.,23 (1987), 559–564.

    Google Scholar 

  11. P. M. Idziak,Undecidability of relatively free Hilbert algebras, Algebra Universalis,25 (1988), 17–26.

    Google Scholar 

  12. P. M.Idziak,Decision problem for relatively free Brouwerian semilattices, to appear in Reports on Mathematical Logic,22 (1988).

  13. P. M. Idziak,Reduced sub-powers and the decision problem for finite algebras in arithmetical varieties, Algebra Universalis,25 (1988), 365–383.

    Google Scholar 

  14. B. Jónsson,Algebras whose congruence lattices are distributive, Math. Scand.,21 (1967), 110–121.

    Google Scholar 

  15. P. Köhler andD. Pigozzi,Varieties with equationally definable principal congruences, Algebra Universalis,11 (1980), 213–219.

    Google Scholar 

  16. M. O. Rabin,A simple method for undecidability proofs and some applications, in: Y. Bar-Hillel (ed),Logic, Methodology and Philosophy of Sciences, North Holland, Amsterdam 1965, pp. 58–68.

    Google Scholar 

  17. M. O.Rabin,Decidable Theories, in: J. Barwise ed.,Handbook of Mathematical Logic, North Holland 1977, pp. 595–629.

  18. A. Tarski, A. Mostowski andR. M. Robinson,Undecidable Theories, North-Holland, Amsterdam 1953.

    Google Scholar 

  19. H. Werner,Discriminator algebras, Studien zur Algebra und ihre Anwendungen, Band 6, Akademie-Verlag, Berlin 1978.

    Google Scholar 

  20. A. P. Zamjatin,Varieties of associative rings whose elementary theory is decidable, Soviet Math. Dokl.,17 (1976), 996–999.

    Google Scholar 

  21. A. P. Zamjatin,Prevarieties of associative rings whose elementary theory is decidable, Sib. J. Math.,19 (1978), 890–901.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This paper was prepared while the author was staying at the Faculty of Integrated Arts and Sciences of the Hiroshima University. He would like to thank Professor Hiroakira Ono for his hospitality.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Idziak, P.M. The decision problem for finite algebras from arithmetical varieties with equationally definable principal congruences. Algebra Universalis 26, 33–47 (1989). https://doi.org/10.1007/BF01243871

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01243871

Keywords

Navigation