Skip to main content
SpringerLink
Log in

Henkin’s Completeness Proof and Glivenko’s Theorem

  • Chapter
The Life and Work of Leon Henkin

Part of the book series: Studies in Universal Logic ((SUL))

  • 716 Accesses

Abstract

We observe that Henkin’s argument for the completeness theorem yields also a classical semantic proof of Glivenko’s theorem and leads in a straightforward way to the weakest intermediate logic for which that theorem still holds. Some refinements of the completeness theorem can also be obtained.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

References

  1. Van Dalen, D.: Intuitionistic logic. In: Handbook of Philosophical Logic, vol. III, pp. 225–339. Reidel, Dordrecht (1986)

    Chapter  Google Scholar 

  2. Gabbay, D.M.: Applications of trees to intermediate logics. J. Symb. Log. 37(1), 135–138 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  3. Parlamento, F.: Truth-value semantics and functional extensions for classical logic of partial terms based on equality. Notre Dame J. Form. Log. 55(3), 383–395 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Rauszer, C.: Formalizations of intermediate logics, Part I. In: Methods in Mathematical Logic—Proceedings of the Sixth Latin American Symposium, Caracas, 1983, Lecture Notes in Mathematics, vol. 1130, pp. 360–384. Springer, Berlin (1985)

    Google Scholar 

  5. Seldin, J.P.: On the proof theory of the intermediate logic MH. J. Symb. Log. 51(3), 626–647 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Smullyan, R.: First-Order Logic. Springer, Berlin (1968)

    Book  MATH  Google Scholar 

  7. Umezava, T.: On logics intermediate between intuitionistic and classical logic. J. Symb. Log. 24(1), 141–153 (1959)

    Article  Google Scholar 

Download references

Acknowledgements

Work supported by funds PRIN-MIUR of Italy.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Udine, via Delle Scienze 206, 33100, Udine, Italy

    Franco Parlamento

Authors
  1. Franco Parlamento
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Franco Parlamento .

Editor information

Editors and Affiliations

  1. Department of Philosophy, Logic and Aesthetics, University of Salamanca, Salamanca, Spain

    María Manzano

  2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    Ildikó Sain

  3. Department of Logic and Philosophy of Science, Autonomous University of Madrid, Madrid, Spain

    Enrique Alonso

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Parlamento, F. (2014). Henkin’s Completeness Proof and Glivenko’s Theorem. In: Manzano, M., Sain, I., Alonso, E. (eds) The Life and Work of Leon Henkin. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09719-0_15

Download citation

Publish with us

Policies and ethics

Search

Navigation