Skip to main content
SpringerLink
Log in

Beth's and Craig's properties via epimorphisms and amalgamation in algebraic logic

  • Conference paper
  • First Online:
Algebraic Logic and Universal Algebra in Computer Science (ALUACS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 425))

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H.Andréka-S.D.Comer-I.Németi, Epimorphisms in cylindric algebras, Preprint (1982).

    Google Scholar 

  2. H.Andréka-B.Jónsson-I.Németi, Relatively free relation algebras, submitted to Proc. Conf. on Algebraic Logic and Universal Algebra in Computer Science, Ames (USA), 1988.

    Google Scholar 

  3. J.Barwise-S.Feferman (Eds.), Model-Theoretic Logics, Springer-Verlag (1985), xviii+893pp.

    Google Scholar 

  4. C.Bergman-R.McKenzie, On the relationship of AP, RS, and CEP in congruence modular varieties. II., Preprint (1987).

    Google Scholar 

  5. S.D. Comer, Classes without the amalgamation property, Pacific J. Math. Vol 28 (1969), 309–318.

    MATH  MathSciNet  Google Scholar 

  6. S.D.Comer, Epimorphisms in discriminator varieties, In: Lectures in Universal Algebra (Colloq. Math. Soc. J. Bolyai Vol 43), Eds.: L.Szabó, Á.Szendrei, North-Holland (1986), 41–48.

    Google Scholar 

  7. A. Daigneault, Freedom in polyadic algebras and two theorems of Beth and Craig, Michigan J. Math. Vol 11 (1964), 129–135.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Goldblatt, Varieties of Complex Algebras, Preprint Victoria University, New Zealand (1988).

    Google Scholar 

  9. P. R. Halmos, Algebraic Logic, Chelsea Publishing Co., New York (1962), 271pp.

    MATH  Google Scholar 

  10. L.Henkin-J.D.Monk-A.Tarski, Cylindric Algebras Part I and Part II, North-Holland (1985).

    Google Scholar 

  11. H.Herrlich-G.E.Strecker, Category Theory, Allyn and Bacon Inc. (1973).

    Google Scholar 

  12. J.S. Johnson, Amalgamation of polyadic algebras, Transactions of the American Math. Society Vol 149 (June 1970), 627–652.

    Article  MATH  Google Scholar 

  13. B.Jónsson, Extensions of relational structures, In: The theory of models. Eds.: J.W.Addison, L.Henkin, A.Tarski, North-Holland (1965), 146–157.

    Google Scholar 

  14. H.J.Keisler, A complete first-order logic with infinitary predicates, Fundamenta Mathematicae Vol 52 (1963),.

    Google Scholar 

  15. E.W. Kiss-L. Márki-P. Pröhle-W. Tholen, Categorical algebraic properties. Compendium on amalgamation, congruence extension, epimorphisms, residual smallness, and injectivity, Studia Sci. Math. Hungar. Vol 18 (1983), 79–141.

    MATH  Google Scholar 

  16. R.J. Maddux, Some varieties containing relation algebras, Trans. Amer. Math. Soc. Vol 272 (1982), 501–526.

    Article  MATH  MathSciNet  Google Scholar 

  17. R.J.Maddux, Pair-dense relation algebras, Submitted.

    Google Scholar 

  18. J.A.Makowsky, Compactness, Embeddings and Definability, in [3] (1985), 645–716.

    Google Scholar 

  19. L.L. Maksimova, Craig's theorem in superintuitionistic logics and amalgamated varieties of pseudo-Boolean algebras, Algebra i logika Vol 16 (1977), 643–681.

    MATH  MathSciNet  Google Scholar 

  20. R. McKenzie, The representation of relation algebras, Doctoral Dissertation, University of Colorado, Boulder (1966), vi+128pp.

    Google Scholar 

  21. J.D. Monk, Studies in cylindric algebra, Doctoral Dissertation, University of California, Berkeley (1961), vi+83pp.

    Google Scholar 

  22. J.D. Monk, Singulary cylindric and polyadic equality algebras, Trans. Amer. Math. Soc. Vol 112 (1964), 185–205.

    Article  MATH  MathSciNet  Google Scholar 

  23. I.Németi, Surjectiveness of epimorphisms is equivalent to Beth definability property in general algebraic logic, Manuscript (1984).

    Google Scholar 

  24. I. Németi, Cylindric-relativized set algebras have strong amalgamation, The Journal of Symbolic Logic Vol 50, No 3 (Sept. 1985), 689–700.

    Article  MATH  MathSciNet  Google Scholar 

  25. I.Németi, Decidability of the equational theory of cylindric relativized set algebras, Preprint, Math. Inst. Hungar. Acad. Sci. (Also available as a chapter of [26].) (1985).

    Google Scholar 

  26. I. Németi, Free algebras and decidability in algebraic logic, Dissertation for DSc with the Hungarian Academy of Sciences, Budapest (1985).

    Google Scholar 

  27. I.Németi, Logic with three variables has Gödel's incompleteness property — thus free cylindric algebras are not atomic, Math. Inst. Hungar. Acad. Sci., Preprint No 49/85 (1985).

    Google Scholar 

  28. I. Németi, Epimorphisms and definability in relation-, polyadic-, and related algebras, Invited lecture at the “Algebraic Logic in Comp. Sci.” Conference, Ames, Iowa (USA) June 1988. (Also available as Seminar Notes for the Algebra Seminar in Ames, Fall 1987.) (1988).

    Google Scholar 

  29. H. Ono, Interpolation and the Robinson property for logics not closed under the Boolean operations, Algebra Universalis 23 (1986), 111–122.

    Article  MATH  MathSciNet  Google Scholar 

  30. D. Pigozzi, Amalgamation, congruence-extension, and interpolation properties in algebras, Algebra Universalis Vol 1 fasc.3 (1972), 269–349.

    MATH  MathSciNet  Google Scholar 

  31. I.Sain, Strong amalgamation and epimorphisms of cylindric algebras and Boolean algebras with operators, Math. Inst. Hungar. Acad. Sci., Preprint No 17/82. Conditionally accepted by Studia Logica (1982).

    Google Scholar 

  32. A. Tarski-S. Givant, A formalization of set theory without variables, American Mathematical Society, Colloquium Publications Vol 41 (1987).

    Google Scholar 

  33. A. Wroński, On a form of equational interpolation property, Foundations in logic and linguistics. Problems and solutions, Selected contributions to the 7th International Congress, Plenum Press, London (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, Pf.127, H-1364, Budapest, Hungary

    Ildikó Sain

Authors
  1. Ildikó Sain
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Clifford H. Bergman Roger D. Maddux Don L. Pigozzi

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sain, I. (1990). Beth's and Craig's properties via epimorphisms and amalgamation in algebraic logic. In: Bergman, C.H., Maddux, R.D., Pigozzi, D.L. (eds) Algebraic Logic and Universal Algebra in Computer Science. ALUACS 1988. Lecture Notes in Computer Science, vol 425. Springer, New York, NY. https://doi.org/10.1007/BFb0043086

Download citation

  • DOI: https://doi.org/10.1007/BFb0043086

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97288-6

  • Online ISBN: 978-0-387-34804-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation