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Relating ordinals to proofs in a perspicuous way

from PART I - PROOF THEORETIC ANALYSIS

Published online by Cambridge University Press:  31 March 2017

Wilfried Sieg
Affiliation:
Carnegie Mellon University, Pennsylvania
Richard Sommer
Affiliation:
Stanford University, California
Carolyn Talcott
Affiliation:
Stanford University, California
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Reflections on the Foundations of Mathematics
Essays in Honor of Solomon Feferman
, pp. 37 - 59
Publisher: Cambridge University Press
Print publication year: 2002

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References

[1] Peter, Aczel, A new approach to the Bachmann method for describing large countable ordinals, unpublished.
[2] Toshiyasu, Arai, Proof theory for theories of ordinals II: Σ1-stability, Preprint (1997).
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[6] Wilfried, Buchholz, The Ω_+1-rule, Iterated inductive definitions and subsystems of analysis: Recent proof- theoretical studies (W., Buchholz, S., Feferman, W., Pohlers, and W., Sieg, editors), Lecture Notes in Mathematics, vol. 897, Springer, 1981, pp. 188-233.
[7] Wilfried, Buchholz, Ordinal analysis of ID_, Iterated inductive definitions and subsystems of analysis: Recent proof-theoretical studies (W., Buchholz, S., Feferman,W., Pohlers, andW., Sieg, editors), Lecture Notes inMathematics, vol. 897, Springer, 1981, pp. 234-260.
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[11] Solomon, Feferman, Proof theory: A personal report, Proof theory (2nd edition) (G., Takeuti, editor), Studies in Logic and the Foundations of Mathematics, North-Holland, 1987, pp. 447-485.
[12] Gerhard, J äger, _-inaccessible ordinals, collapsing functions and a recursive notation system, Archiv für mathematische Logik, vol. 24 (1984), pp. 49-62.Google Scholar
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[14] Wolfram, Pohlers, Ordinal notations based on a hierarchy of inaccessible cardinals, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 157-179.Google Scholar
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[16] Michael, Rathjen, Ordinal notations based on a weakly Mahlo cardinal, Archive for Mathematical Logic, vol. 29 (1990), pp. 249-263.Google Scholar
[17] Michael, Rathjen, Proof theory of reflection, Annals of Pure and Applied Logic, vol. 68 (1994), pp. 181- 224.Google Scholar
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[19] Anton, Setzer, Well-ordering proofs for Martin-Löf type theory, Annals of Pure and Applied Logic, vol. 92 (1998), pp. 113-159.Google Scholar

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