Skip to main content

Hilbert’s ε-Symbol in the Presence of Generalized Quantifiers

  • Chapter
Quantifiers: Logics, Models and Computation

Part of the book series: Synthese Library ((SYLI,volume 249))

Abstract

The so called Hilbert’s ε-symbol transforms a formula φ(x) in a term εx φ(x) with the intended meaning: “some x such that φ(x), if such x exists, an arbitrary individual, otherwise”.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Asser, Theorie der logischen Auswahlfunktionen, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 3 (1957), pp. 30–68.

    Google Scholar 

  2. W. Ackermann, Megentheoretische Begrundung der Logik,Mathematische Annalen 115 (1937–8), pp. 1–22.

    Google Scholar 

  3. J. Barwise, Admissible sets and structures, Springer Verlag, 1975.

    Google Scholar 

  4. N. Bourbaki, Elements des Mathématiques. Libre I (Theorie des ensembles), Cap I, II. Hermann, Paris, 1954.

    Google Scholar 

  5. X. Caicedo, Definability properties and the congruence closure, Archive for Mathematical Logic 30 (1990), pp. 231–240.

    Google Scholar 

  6. J. Corcoran, W. S. Hatcher and J. Herring, Variable binding term operators, Zeitschrift für Mathematische Logic und Grundlagen der Mathematik 18 (1972), pp. 177–186.

    Google Scholar 

  7. N. D. A. Da Costa, Model theoretical approach to variable binfing term operators, In Mathematical Logic in Latin America, North-Holland, 1980, pp. 133–162.

    Google Scholar 

  8. H. D. Ebbinghaus, Extended logics: the general framework, In Model Theoretic Logics, J. Barwise, S. Feferman (eds.), Springer Verlag, 1985.

    Google Scholar 

  9. D. Hilbert, Die Grundlagen der Mathematik, Address at the Hamburg Mathematical Seminar (translation in From Frege to Góde1, J. van Heijenort (ed. ), Harward University Press, 1927.

    Google Scholar 

  10. D. Hilbert and P. Bernays, Grundlagen der Mathematik, Vol. 2, Springer Verlag, 1939.

    Google Scholar 

  11. A. C. Leisenring, Mathematical Logic and Hilbert’s ε-symbol, Macdonald Technical and Scientific, London, 1969.

    Google Scholar 

  12. A. H. Mekler and S. Shelah, Stationary logic and its friends. I, Notre Dame Journal of Formal Logic 26 (1985), pp. 129–138.

    Google Scholar 

  13. C. H. Stlnchez, Aspectos da eliminabilidade dos operadores nomínaís, Tese de Doutorado, Universidade Estadual de Campinas, Sao Paulo, 1988.

    Google Scholar 

  14. D. Scott, Existence and description in formal logic, In Bertrand Russell, Philosopher of the Century, Little, Brown and Co., Boston, 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Caicedo, X. (1995). Hilbert’s ε-Symbol in the Presence of Generalized Quantifiers. In: Krynicki, M., Mostowski, M., Szczerba, L.W. (eds) Quantifiers: Logics, Models and Computation. Synthese Library, vol 249. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0524-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0524-0_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4540-9

  • Online ISBN: 978-94-017-0524-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics