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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
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Logic Colloquium '98 , pp. 426 - 448
Publisher: Cambridge University Press
Print publication year: 2000

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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.
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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.
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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.

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