Skip to main content
Springer Nature Link
Log in

A representation theorem for languages with generalized quantifiers through back-and-forth methods

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We obtain in this paper a representation of the formulae of extensions ofL ωω by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedo's version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. X. Caicedo,Back-and-forth system arbitrary quantifiers,Mathematical Logic in Latin America, A. I. Arruda, R. Chuaqui, N.C.A. da Costa (eds.), North-Holland Publishing Company, 1980, pp. 83–102.

  2. C. Chang andH. J. Keisler,Model Theory, North-Holland, 1976.

  3. A. Ehrenfeucht,An application of games to the completeness problem for formalized theories,Fundamenta Mathematica, vol. XLIV (1961).

  4. C. H. Ehresmann,Categories inductives at pseudogroupes,Ann. Inst. Fourier, 10 (1960), pp. 307–336.

    Google Scholar 

  5. R. Fraïsse Cours de Logique Mathématique, Tóme 2, Théorie des modéles, Gauthier-Villars, 1972.

  6. A. M. Sette andS. Sette,Functionalization of first-order languages with finitely many predicates,Proceedings of the First Brazilian Conference in Mathematical Logic, A. I. Arruda, N.C.A. da Costa, R. Chuaqui (eds.), Marcel Decker 1978, pp. 7–11.

  7. A. M. Sette,Partial isomorphisms extension method and a representation theorem for Post-language, to be published in theZeitschrift für Mathematische Logik and Grundlagen der Mathematik.

  8. A. M. Sette,Modal logic: Back-and-forth method and (functional) representation theorem, to be published.

  9. I. M. Singer andStemberg,The infinite groups of Lie and Cartan (Introduction ana definition of pseudogroup),Journal D'Analyse Mathematique, vol. XV, 1965, pp. 1–114.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universita Estadual de Campinas, Caixa Postal 1170, 13100, Campinas SP, Brasil

    Renato H. L. Pedrosa & Antonio M. A. Sette

Authors
  1. Renato H. L. Pedrosa
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Antonio M. A. Sette
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pedrosa, R.H.L., Sette, A.M.A. A representation theorem for languages with generalized quantifiers through back-and-forth methods. Stud Logica 47, 401–411 (1988). https://doi.org/10.1007/BF00671569

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00671569

Keywords