Skip to main content
Log in

Applications Of Elementary Submodels In General Topology

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

Elementary submodels of some initial segment of the set-theoretic universe are useful in order to prove certain theorems in general topology as well as in algebra. As an illustration we give proofs of two theorems due to Arkhangel’skii concerning cardinal invariants of compact spaces.

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.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Bandlow, I.: 1991, ‘A Construction in Set-theoretic Topology by Means of Elementary Substructures’, Zeitschrift für Mathematische Logik 37, 467–480.

    Google Scholar 

  • Chang, C. C. and Keisler, J.: 1990, Model Theory, Amsterdam [Studies in Logic and the Foundations of Mathematics 73].

  • Dow, A.: 1988, ‘An Introduction to Applications of Elementary Submodels to Topology’, Topology Proceedings 13, 17–72.

    Google Scholar 

  • Eklof, P. and Mekler, A.: 1990, Almost Free Modules, Amsterdam [North-Holland Mathematical Library 46].

  • Engelking, R.: 1977. General Topology, Warszawa [Polska Akademie Nauk, Monographie Matematyczne 60].

  • Fuchino, S., Geschke, S., and Soukup, L.: 2001, ‘On the Weak Freese-Nation Property of \(P\)(ω)', Archive for Mathematical Logic 40, 425–435.

    Google Scholar 

  • Fuchino, S. and Soukup, L.: 1997, ‘More Set Theory Around the Weak Freese-Nation Property’, Fundamenta Mathematicae 154, 159–176.

    Google Scholar 

  • Juhasz, I.: 1980, Cardinal Functions in Topology: Ten Years Later, Amsterdam [Mathematical Centre Tracts 123].

  • Just, W. and Weese, M.: 1997, Discovering Modern Set Theory II: Set-theoretic Tools for Every Mathematician, Providence [American Mathematical Society, Graduate Studies in Mathematics 18].

  • Kunen, K.: 1980, Set Theory, Amsterdam [Studies in Logic and the Foundations of Mathematics 102].

  • Mekler, A. and Shelah, S.: 1993, ‘Some Compact Logics — Results in ZFC’, Annals of Mathematics 137, 221–248.

    Google Scholar 

  • Ščcepin, V.: 1981, ‘Functors and Uncountable Powers of Compacts’, Russian Mathematical Surveys 36, 1–71.

    Google Scholar 

  • Shelah, S.: Non Structure Theory, (in preparation).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Geschke, S. Applications Of Elementary Submodels In General Topology. Synthese 133, 31–41 (2002). https://doi.org/10.1023/A:1020819407308

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020819407308

Keywords

Navigation