Skip to main content
SpringerLink
Log in

Two First-Order Theories of Ordinals

  • Conference paper
  • First Online:
Fields of Logic and Computation III

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12180))

  • 349 Accesses

Abstract

This paper compares a first-order theory of ordinals proposed by the author to the theory published 1965 by Gaisi Takeuti. A clarification of the relative deductive strength of the two theories is 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. Ahrendt, W., Beckert, B., Bubel, R., Hähnle, R., Schmitt, P.H., Ulbrich, M. (eds.): Deductive Software Verification - The KeY Book - From Theory to Practice. LNCS, 10001st edn. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49812-6

    Book  Google Scholar 

  2. Bachmann, H.: Transfinite Zahlen. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 1, 2nd edn. Springer, Berlin (1967). https://doi.org/10.1007/978-3-642-88514-3

    Book  MATH  Google Scholar 

  3. Schmitt, P.H.: A mechanizable first-order theory of ordinals. In: Schmidt, R.A., Nalon, C. (eds.) TABLEAUX 2017. LNCS (LNAI), vol. 10501, pp. 331–346. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66902-1_20

    Chapter  Google Scholar 

  4. Schmitt, P.H.: Takeuti’s first-order theory of ordinals revisited. Technical report 2, Department of Informatics, Karlsruhe Institute of Technology (2018)

    Google Scholar 

  5. Takeuti, G.: On the theory of ordinal number, s ii. J. Math. Soc. Japan 10, 106–120 (1958)

    Article  MathSciNet  Google Scholar 

  6. Takeuti, G.: A formalization of the theory of ordinal numbers. J. Symb. Logic 30, 295–317 (1965)

    Article  MathSciNet  Google Scholar 

  7. Ulbrich, M.: Dynamic Logic for an intermediate language: verification, interaction and refinement. Ph.D. thesis, Karlsruhe Institute of Technology, June 2013. http://nbn-resolving.org/urn:nbn:de:swb:90-411691

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, Karlsruhe Institute of Technology (KIT), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Peter H. Schmitt

Authors
  1. Peter H. Schmitt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter H. Schmitt .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Andreas Blass

  2. Université Paris Est Créteil, Fontainebleau, France

    Patrick Cégielski

  3. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Nachum Dershowitz

  4. Fakultät für Mathematik und Informatik, Universität Leipzig, Leipzig, Germany

    Manfred Droste

  5. Reactive Systems Group, Universitat des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Schmitt, P.H. (2020). Two First-Order Theories of Ordinals. In: Blass, A., Cégielski, P., Dershowitz, N., Droste, M., Finkbeiner, B. (eds) Fields of Logic and Computation III. Lecture Notes in Computer Science(), vol 12180. Springer, Cham. https://doi.org/10.1007/978-3-030-48006-6_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-48006-6_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-48005-9

  • Online ISBN: 978-3-030-48006-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation