Skip to main content

Monadicity in topological pseudo-boolean algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 1103)

Keywords

  • Modal Logic
  • Closure Operator
  • Deductive System
  • Regular Element
  • Open Element

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   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
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. O. Becker, Zur Logik der Modalitäten, Jahrbuch für Philosophie und Phänomenologische Forschung 11 (1930) 497–548.

    MATH  Google Scholar 

  2. E. Beth and J.F.F. Nieland, Semantic Construction of Lewis Systems S4 and S5, in: Addison, Henkin, Tarski, eds., The Theory of Models (North-Holland, Amsterdam, 1965) 17–24.

    Google Scholar 

  3. D.J. Brown and R. Suzsko, Abstract Logics, Diss. Math. CII (1973) 9–40.

    Google Scholar 

  4. R.A. Bull, Some modal calculi based on IC, in: Crossley and Dummett, eds., Formal Systems and Recursive Functions (North-Holland, Amsterdam, 1965) 3–7.

    CrossRef  Google Scholar 

  5. —, A modal extension of intuitionist logic, Notre Dame J. Formal Logic 6 (1965) 142–145.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. C. Davis, Modal operators, equivalence relations and projective algebras, Am. J. Math. 76 (1954) 747–762.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. G. Fischer-Servi, On modal logic with an intuitionistic base, Studia Logica 36 (1977) 141–149.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. —, Semantics for a class of intuitionistic modal calculi, in: Dalla Chiara, ed., Italian Studies in the Philosophy of Science (Reidel, Dordrecht, 1980) 59–72.

    CrossRef  Google Scholar 

  9. —, An intuitionistic analogue of S4 as a logical modeling for science, J. Philos. Logic, to appear.

    Google Scholar 

  10. J. M. Font, Implication and deduction in some intuitionistic modal logics, Rep. Math. Logic 17 (1983) to appear.

    Google Scholar 

  11. K. Gödel, Eine Interpretation des Intuitionistischen Aussagenkalküls, Ergebnisse eines Mathematischen Kolloquiums 4 (1933) 39–40.

    MATH  Google Scholar 

  12. P.R. Halmos, Algebraic Logic I: Monadic Boolean algebras, Compos. Math. 12 (1955) 217–249.

    MathSciNet  Google Scholar 

  13. A. Monteiro, La semisimplicité des algèbres de Boole topologiques et les systèmes déductifs, Rev. Union Mat. Argent. 25 (1971) 417–448.

    MathSciNet  MATH  Google Scholar 

  14. J.C.C. McKinsey and A. Tarski, On closed elements in closure algebras, Ann. Math. 47 (1946) 122–162.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. H. Ono, On some intuitionistic modal logics, Publ. Res. Inst. Math. Sci. Kyoto Univ. 13 (1977) 687–722.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. A.N. Prior, Time and Modality (Oxford Univ. Press, 1957).

    Google Scholar 

  17. —, Formal Logic (Oxford Univ. Press, 1962).

    Google Scholar 

  18. H. Rasiowa, An algebraic approach to non-classical logics (North-Holland, Amsterdam, 1974).

    MATH  Google Scholar 

  19. H. Rasiowa and R. Sikorski, The mathematics of the metamathematics (P.W.N., Warszawa, 1970).

    MATH  Google Scholar 

  20. V. Verdú, Distributive and Boolean logics. Stochastica 3 (1979) 97–108.

    MathSciNet  MATH  Google Scholar 

  21. G.H. von Wright, An essay in modal logic (North-Holland, Amsterdam, 1951).

    MATH  Google Scholar 

  22. M. Wajsberg, Ein erweiterter Klassenkalkül, Monatsh. Math. Phys. 40 (1933) 113–126.

    CrossRef  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

© 1984 Springer-Verlag

About this paper

Cite this paper

Font, J.M. (1984). Monadicity in topological pseudo-boolean algebras. In: Müller, G.H., Richter, M.M. (eds) Models and Sets. Lecture Notes in Mathematics, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099386

Download citation

  • DOI: https://doi.org/10.1007/BFb0099386

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13900-3

  • Online ISBN: 978-3-540-39115-9

  • eBook Packages: Springer Book Archive