Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-24T04:48:00.863Z Has data issue: false hasContentIssue false

Ordinal Systems, Part 2: One Inaccessible

Published online by Cambridge University Press:  31 March 2017

Anton Setzer
Affiliation:
Uppsala University
Samuel R. Buss
Affiliation:
University of California, San Diego
Petr Hájek
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Pavel Pudlák
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Get access
Type
Chapter
Information
Logic Colloquium '98 , pp. 426 - 448
Publisher: Cambridge University Press
Print publication year: 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. W., Buchholz. Normalfunktionen und konstruktive Systeme von Ordinalzahlen. In J., Diller and G.H., Müller, editors, Proof Theory Symposion, Kiel 1974, volume 500 of Springer Lecture Notes in Mathematics, pages 4 – 25, Berlin, Heidelberg, New York, 1975. Springer.
2. W., Buchholz. A new system of proof-theoretic ordinal functions. Ann. Pure a. Appl. Logic, 32:195–207, 1986.Google Scholar
3. W., Buchholz. Wellordering proofs for systems of fundamental sequences. Draft, München, 1990.
4. W., Buchholz. A simplified version of local predicativity. In P., Aczel, H., Simmons, and S.S., Wainer, editors, Proof Theory. A selection of papers from the Leeds Proof Theory Programme 1990, pages 115–147, Cambridge, 1992. Cambridge University Press.
5. W., Buchholz and K., Schütte. Proof Theory of Impredicative Subsystems of Analysis. Bibliopolis, Naples, 1988.
6. J.-Y., Girard. Proof theory and logical complexity. Handwritten notes, 1135 pp.
7. J.-Y., Girard. Π_1/2-Logic, part 1: Dilators. Ann. Pure a. Appl. Logic, 21:75–219, 1981.Google Scholar
8. G., Jäger. A well-ordering proof for Feferman's theory T0. Arch. math. Logic, 23:65–77, 1983.Google Scholar
9. G., Jäger. Theories for Admissible Sets: A Unifying Approach to Proof Theory. Bibliopolis, Naples, 1986.
10. P., Martin-Löf. Intuitionistic type theory. Bibliopolis, Naples, 1984.
11. W., Pohlers. Proof Theory. An introduction, volume 1407 of Springer Lecture Notes in Mathematics. Springer, Berlin, Heidelberg, New York, 1989.
12. M., Rathjen. How to develop proof–theoretic ordinal functions on the basis of admissible ordinals. Mathematical Logic Quarterly, 39(1):47–54, 1993.
13. M., Rathjen and A., Weiermann. Proof–theoretic investigations on Kruskal's theorem. Annals of Pure and Applied Logic, 60:49–88, 1993.Google Scholar
14. K., Schütte. Kennzeichnung von Ordinalzahlen durch rekursiv definierte Funktionen. Math. Ann., 127:16–32, 1954.Google Scholar
15. A., Setzer. Proof theoretical strength of Martin-Löf Type Theory with W-type and one universe. PhD thesis, Universität München, 1993.
16. A., Setzer. An introduction to well-ordering proofs in Martin-L öf's type theory. In G., Sambin and J., Smith, editors, Twenty-five years of constructive type theory, pages 245–263, Oxford, 1998. Clarendon Press.
17. A., Setzer.Well-ordering proofs forMartin-Löf type theory. Annals of Pure andApplied Logic, 92:113–159, 1998.Google Scholar
18. A., Setzer. Ordinal systems. To appear in: B., Cooper, J., Truss, editors, Sets and Proofs, Cambridge University Press, 1999.

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×