Skip to main content
SpringerLink
Log in

On Amalgamation in Algebras of Logic

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We show that not all epimorphisms are surjective in certain classes of infinite dimensional cylindric algebras, Pinter's substitution algebras and Halmos' quasipolyadic algebras with and without equality. It follows that these classes fail to have the strong amalgamation property. This answers a question in [3] and a question of Pigozzi in his landmark paper on amalgamation [9]. The cylindric case was first proved by Judit Madarasz [7]. The proof presented herein is substantially different. By a result of Németi, our result implies that the Beth-definability Theorem fails for certain expansions of first order logic

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ahmed, T. S., On Neat Reducts of Algebras of Logic, PhD thesis, Cairo University, 2002.

  2. Ahmed, T. S., ‘On Amalgamation of Reducts of Polyadic Algebras’, Algebra Universalis, 51:301–359, 2004.

    Article  Google Scholar 

  3. Ahmed, T. S., and I. Németi, On Neat Reducts of Algebras of Logic. Studia Logica, 68:229–262, 2001.

  4. Henkin, L., J.D. Monk, and A. Tarski, Cylindric Algebras Parts I and II, North–Holland, Amsterdam, 1971 and 1985.

  5. Hoogland, E., Definability and Interpolation (Model theoretic investigations), PhD thesis, Institute for Logic, Language and Computation, University of Amsterdam, 2001. ILLC Dissertation Series DS-2001-05, xii+209 pp.

  6. Madarasz, J., and T. Sayed Ahmed, Amalgamation, interpolation and epimorphisms, solutions to all problems of Pigozzi, and some more, preprint of the Mathematical institute of the Hungarian Academy of Sciences.

  7. Madarasz, J., ‘Surjectiveness of epimorphisms in varities of Algebraic Logic’, submitted.

  8. Németi, I., ‘Algebraization of Quantifier Logics, an Introductory Overview’, Technical Report 13/1996, Math. Inst. Hungar. Acad. Sci., 1996. A shorter and older version appeared in Studia Logica, 50:485–570, 1991. Electronically available as: http://circle.math-inst.hu/pub/algebraic-logic/survey.dvi, survey.ps.

  9. Pigozzi, D. L., ‘Amalgamation, congruence-extensions, and interpolation properties in algebras’, Algebra Universalis, 1, fasc.3:269–349, 1972.

  10. Sain, I., and R. J. Thompson, ‘Strictly Finite Schema Axiomatization of Quasipolyadic Algebras’, in J. D. Monk H. AndrŽka, and I. Németi, (eds.), Algebraic Logic (Proc. Conf. Budapest 1988), volume 54 of Colloq. Math. Soc. János Bolyai, North–Holland, Amsterdam, 1991, pp. 539–571.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    Tarek Sayed Ahmed

Authors
  1. Tarek Sayed Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tarek Sayed Ahmed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ahmed, T.S. On Amalgamation in Algebras of Logic. Stud Logica 81, 61–77 (2005). https://doi.org/10.1007/s11225-005-2802-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-005-2802-9

Keywords

Search

Navigation