Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-direct-independence-proof-of-buchholz-s-hydra-game-on-finite-labeled-tZIw0gcmKi
References (7)
-
T. Arai (1984)
An accessibility proof of ordinal diagrams in intuitionistic theories for iterated inductive definitionsTsukuba journal of mathematics, 8
-
E. Cichon (1983)
A short proof of two recently discovered independence results using recursion theoretic methods, 87
-
L. Kirby, J. Paris (1982)
Accessible Independence Results for Peano ArithmeticBulletin of The London Mathematical Society, 14
-
M. Okada (1988)
Note on a Proof of the Extended Kirby - Paris Theorem on Labeled Finite TreesEur. J. Comb., 9
-
Jussi KETONENt, Robert SOLOVAYtt (1981)
Rapidly growing Ramsey functionsAnnals of Mathematics, 113
-
M. Hamano, M. Okada (1995)
A Relationship Among Gentzen's Proof‐Reduction, Kirby‐Paris' Hydra Game and Buchholz's Hydra GameMathematical Logic Quarterly, 43
-
M. Okada (1987)
A simple relationship between Buchholz's new system of ordinal notations and Takeuti's system of ordinal diagramsJournal of Symbolic Logic, 52
- Publisher
- Springer Journals
- Copyright
- Copyright © 1998 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s001530050084
- Publisher site
- See Article on Publisher Site
Abstract
We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of $(\Pi^{1}_{1}-CA) + BI$ and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Mar 1, 1998