Skip to main content
Log in

Ordinal notations based on a weakly Mahlo cardinal

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Buchholz, W.: Normalfunktionen und konstruktive Systeme von Ordinalzahlen. Proof Theory Symposium Kiel 1974. (Lect. Notes Math., vol. 500, pp. 4–25) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  2. Buchholz, W.: Ordinal analysis of IDv. In: Buchholz, W., Feferman, S., Pohlers, W., Sieg, W. (eds.) Iterated inductive definitions and subsystems of analysis. (Lect Notes Math., vol. 897, pp. 243–260) Berlin Heidelberg New York: Springer 1981

    Google Scholar 

  3. Buchholz, W.: A new system of proof-theoretic ordinal functions. Arch. Math. Logik Grundlagenforsch.32, 195–207 (1986)

    Google Scholar 

  4. Buchholz, W., Schütte, K.: Ein Ordinalzahlensystem für die beweistheoretische Abgrenzung derπ 12 -Separation und Bar-Induktion. Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse (1983)

  5. Buchholz, W., Schütte, K.: Proof theory of impredicative subsystems of analysis. Naples: Bibliopolis 1988

    Google Scholar 

  6. Drake, F.R.: Set Theory. An introduction to large cardinals. Amsterdam: North-Holland 1974

    Google Scholar 

  7. Harrington, L.: The superjump and the first recursively Mahlo ordinal. In: Gandy, R.O., Yates, C.E.M. (eds.) Logic Colloquium '69, pp. 43–52. Amsterdam: North-Holland 1971

    Google Scholar 

  8. Jäger, G.:ϱ-inaccessible ordinals, collapsing functions and a recursive notation system. Arch. Math. Logik Grundlagenforsch.24, 49–62 (1984)

    Google Scholar 

  9. Jäger, G., Pohlers, W.: Eine beweistheoretische Untersuchung von (δ 12 −CA) + (BI) und verwandter Systeme. Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse (1982)

  10. Jech, T.: Set theory. New York San Francisco London: Academic Press 1978

    Google Scholar 

  11. Pohlers, W.: Ordinal notations based on a hierarchy of inaccessible cardinals. Ann. Pure Appl. Logic33, 157–179 (1987)

    Google Scholar 

  12. Pohlers, W.: Proof theory: an introduction. Berlin Heidelberg New York: Springer 1989 (to appear)

    Google Scholar 

  13. Richter, W.H.: Recursively Mahlo ordinals and inductive definitions. In: Gandy, R.O., Yates, C.E.M. (eds.) Logic Colloquium '69, pp. 273–288. Amsterdam: North-Holland 1971

    Google Scholar 

  14. Schütte, K.: Proof theory. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  15. Schütte, K.: Eine ErweiterungT(V′) des OrdinalzahlensystemsC Ω Λ 0 von G. Jäger. Arch. Math. Logic27, 85–99 (1988)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rathjen, M. Ordinal notations based on a weakly Mahlo cardinal. Arch Math Logic 29, 249–263 (1990). https://doi.org/10.1007/BF01651328

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01651328

Keywords

Navigation