Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-18T02:38:40.493Z Has data issue: false hasContentIssue false

The Superjump in Martin-Löf Type Theory

Published online by Cambridge University Press:  31 March 2017

Michael Rathjen
Affiliation:
University of Leeds, Leeds
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. 363 - 386
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. P., Aczel: The strength of Martin–Löf's intuitionistic type theory with one universe, in: S., Miettinen, S., Väänänen (eds.): Proceedings of Symposia in Mathematical Logic, Oulu, 1974, and Helsinki, 1975, Report No. 2 (University of Helsinki, Department of Philosophy, 1977) 1–32.
2. P., Aczel: The Type Theoretic Interpretation of Constructive Set Theory, in: MacIntyre, A., Pacholski, L., Paris, J.(eds.), Logic Colloquium '77 (North-Holland, Amsterdam, 1978).
3. P., Aczel: The Type Theoretic Interpretation of Constructive Set Theory: Choice Principles, in: Troelstra, A.S., van Dalen, D.(eds.), The L.E.J. Brouwer Centenary Symposium, (North–Holland, Amsterdam, 1982).
4. P., Aczel: The Type Theoretic Interpretation of Constructive Set Theory: Inductive Definitions, in: Marcus, R.B. et al. (eds), Logic, Methodology, and Philosophy of Science VII, (North–Holland, Amsterdam 1986).
5. J, Barwise: Admissible Sets and Structures, Springer, Berlin 1975.
6. M., Beeson: Recursive Models for Constructive Set Theories, Annals of Math. Logic 23, 126–178 (1982).Google Scholar
7. M., Beeson: Foundations of Constructive Mathematics, (Springer Verlag, Berlin, 1985.
8. P., Dybjer: A general formulation of simultaneous inductive-recursive definitions in type theory (preprint 1994) 21 pages.
9. T., Glas: Partielle Modelle von Theorien imprädikativer Mengenlehre (Master Thesis, University of Münster, 1990).
10. E., Griffor and E., Palmgren: A Intuitionistic Theory of Transfinite Types (preprint 1990) 22 pages.
11. E., Griffor and M., Rathjen: The strength of some Martin–Löf type theories. Archive for Mathematical Logic 33 (1994) 347–385.
12. P., Martin-Löf: An intuitionistic theory of types: predicative part, in: H.E., Rose and J., Sheperdson (eds.): Logic Colloquium '73 (North–Holland, Amsterdam, 1975) 73–118.
13. P., Martin-Löf: Intuitionistic Type Theory, (Bibliopolis, Naples, 1984).
14. B., Nordström, K., Petersson and J.M., Smith: Programming in Martin–Löf's Type Theory, (Clarendon Press, Oxford, 1990).
15. E., Palmgren: Transfinite hierarchies of universes, Department of Mathematics Report 1991:7 (Uppsala University, 1991), 16 pages.
16. E., Palmgren: An information system interpretation of Martin-Löf's partial type theory with universes, Information and Computation 106 (1993) 26–60.
17. E., Palmgren: On universes in type theory. To appear in: Proceedings of “Twenty-five years of type theory”, Venice, 1995 (Oxford University Press).
18. Aarne, Ranta: Type-theoretical grammar (Clarendon Press, Oxford, 1994).
19. M., Rathjen: Untersuchungen zu Teilsystemen der Zahlentheorie zweiter Stufe und der Mengenlehre mit einer zwischen Δ12− CA und Δ12 − CA + BI liegenden Beweisstärke. Publication of the Institute forMathematical Logic and Foundational Research of the University of Münster (1989). Extension of 1988 Münster University doctoral thesis. MR 91m#03062.
20. M., Rathjen: Ordinal notations based on a weakly Mahlo cardinal, Archive for Mathematical Logic 29 (1990) 249–263.Google Scholar
21. M., Rathjen: Proof-Theoretic Analysis of KPM, Arch. Math. Logic 30 (1991) 377–403.Google Scholar
22. M., Rathjen, E., Griffor, E., Palmgren: Inaccessibility in constructive set theory and type theory. Annals of Pure and Applied Logic 94 (1998) 181–200.Google Scholar
23. M., Rathjen: Well-ordering proofs in constructive set theory. In preparation.
24. A., Setzer: Proof theoretical strength of Martin-Löf type theory with W-type and one universe (PhD thesis, Universität München, 1993).
25. A., Setzer: A well-ordering proof for the proof theoretical strength of Martin-Löf type theory. Annals of Pure and Applied Logic 92 (1998) 113–159.Google Scholar
26. A., Setzer: Extending Martin-Löf type theory by one Mahlo-universe, to appear in: Archive for Mathematical Logic.
27. A.S., Troelstra and D., van Dalen: Constructivism in Mathematics: an Introduction, volume II, North–Holland, Amsterdam 1988.

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
×