Skip to main content
SpringerLink
Log in

The Skolem-Löwenheim theorem in toposes

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

The topos theory gives tools for unified proofs of theorems for model theory for various semantics and logics. We introduce the notion of power and the notion of generalized quantifier in topos and we formulate sufficient condition for such quantifiers in order that they fulfil downward Skolem-Löwenheim theorem when added to the language. In the next paper, in print, we will show that this sufficient condition is fulfilled in a vast class of Grothendieck toposes for the general and the existential quantifiers.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. C. Fitting,Intuitionistic Logic, Model Theory and Forcing, North-Holland 1969.

  2. M. P. Fourman, C. J. Mulvey andD. S. Scott,Applications of Sheaf Theory to Algebra, Analysis and Topology, Lecture Notes in Mathematics, Springer-Verlag 1979.

  3. D. Higgs,A category approach to the Boolean-valued set theory, preprint.

  4. P. T. Johnstone,Topos Theory, Academic Press 1977.

  5. P. Lindström,First order predicate logic with generalized quantifiers, Theoria, Vol. 32 (1966) pp. 186–195.

  6. G. Loullis,Sheaves and Boolean-valued model theory The Journal of Symbolic Logic Vol. 44 (1979) pp. 153–183.

    Google Scholar 

  7. S. MacLane,Categories for the Working Mathematician, Graduate Texts in Mathematics 5, Springer-Verlag 1971.

  8. M. Makkai andG. E. Reyes,First Order Categorial Logic, Lecture Notes in Mathematics, Vol. 611, 1977 Springer-Verlag.

  9. H. Rasiowa andR. Sikorski,The Mathematics of Methamathematics, Państwowe Wydawnictwo Naukowe 1963.

  10. G. C. Wraith,Lectures on Elementary Topoi, Model Theory and Topoi, Lectures Notes in Mathematics, Vol. 445 (1975), Springer-Verlag.

Download references

Author information

Authors and Affiliations

  1. The Institute of Mathematics, University of Warsaw, Poland

    Marek Zawadowski

Authors
  1. Marek Zawadowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zawadowski, M. The Skolem-Löwenheim theorem in toposes. Stud Logica 42, 461–475 (1983). https://doi.org/10.1007/BF01371634

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01371634

Keywords

Search

Navigation