Skip to main content

An algebraic proof of the barwise compactness theorem

Part of the Lecture Notes in Mathematics book series (LNM,volume 72)

Keywords

  • Boolean Logic
  • Deductive System
  • Compactness Theorem
  • Closure Property
  • Completeness Theorem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barwise, J., Infinitary logic and admissible sets., Ph.D. Dissertation, Stanford University, 1966.

    Google Scholar 

  2. Barwise, J., Infinitary logic and admissible sets. To appear in The Journal of Symbolic Logic.

    Google Scholar 

  3. Jensen, R. and Karp, C., Primitive recursive set functions. To appear in the Proceedings of the Set Theory Institute, UCLA, Summer, 1967.

    Google Scholar 

  4. Karp, C., Languages with expressions of infinite length, Ph.D. Dissertation, University of Southern California, 1959.

    Google Scholar 

  5. -, Languages with expressions of infinite length, North-Holland Publishing Company, Amsterdam, 1964, 183 pp.

    MATH  Google Scholar 

  6. -, Nonaxiomatizability results for infinitary systems, The Journal of Symbolic Logic, vol. 32 (1967), pp. 367–384.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Kino, A. and Takeuti, G., On predicates with infinitely long expressions, Journal of the Mathematical Society of Japan, vol. 15 (1963), pp. 176–190.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Kreisel, G., Model-theoretic invariants: Applications to recursive and hyperarithmetic operations, The Theory of Models, North-Holland Publishing Company, Amsterdam, 1965, pp. 190–206.

    Google Scholar 

  9. Kreisel, G., Choice of infinitary languages by means of definability criteria: Generalized recursion theory. This volume.

    Google Scholar 

  10. Kripke, S., Transfinite Recursions on admissible ordinals (abstract). The Journal of Symbolic Logic, vol. 29 (1964), p. 161.

    Google Scholar 

  11. Levy, A., A hierarchy of formulas in set theory, Memoirs of the American Mathematical Society, No. 57 (1965), 76 pp.

    Google Scholar 

  12. Scott, D. and Tarski, A., The sentential calculus with infinitely long expressions, Colloquium Mathematicum, vol. 6 (1958), pp. 166–170.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1968 Springer-Verlag

About this paper

Cite this paper

Karp, C. (1968). An algebraic proof of the barwise compactness theorem. In: Barwise, J. (eds) The Syntax and Semantics of Infinitary Languages. Lecture Notes in Mathematics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079684

Download citation

  • DOI: https://doi.org/10.1007/BFb0079684

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04242-6

  • Online ISBN: 978-3-540-35900-5

  • eBook Packages: Springer Book Archive