Proof theory for theories of ordinals - I: Recursively Mahlo ordinals

Annals of Pure and Applied Logic

Volumn 122, Issue 1-3, 2003, Pages 1-85

  Arai, Toshiyasu ^a  

^a KOBE UNIVERSITY   (Japan)

Author keywords

Proof theoretic ordinals; Reflecting ordinals

Indexed keywords

EID: 3543056122     PISSN: 01680072     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-0072(03)00020-4     Document Type: Article

References (14)

1. T. Arai, Proof theory for reflecting ordinals II: recursively Mahlo ordinals, handwritten note, 1989.
2. Arai T. Introduction to finitary analyses of proof figures, in: Cooper S.B. Truss J.K. (Eds.), Sets and Proofs 1999 1-25 Cambridge University Press Cambridge
3. Arai T. Ordinal diagrams for recursively Mahlo universes Arch. Math. Logic 39 2000 353-391
4. Barwise J. Admissible Sets and Structures 1975 Springer Berlin
5. Buchholz W. A note on the ordinal analysis of KPM Oikkonen J. Väänänen J. (Eds.), Logic Colloquium '90 Lecture Notes in Logic Vol. 2 1991 1-9 Springer Berlin
6. Buchholz W. A simplified version of local predicativity (Ed.), Aczel P. et al Proof Theory 1992 115-147 Cambridge University Press Cambridge
7. Gentzen G. Neue Fassung des Widerspruchsfreiheitsbeweises für die reine Zahlen theorie, Forschungen zur Logik und zur Grundlegung der exakter Wissenschaften Neue Folge 4 1938 19-44
8. Jäger G. Zur Beweistheorie der Kripke-Platek Mengenlehre über den natürlichen Zahlen Arch. Math. Logik 22 1982 121-139
9. G. Jäger, W. Pohlers, Eine beweistheoretische Untersuchung von (Δ1/2-CA) + BI und verwandter Systeme, Sitzungsber. d. Bayer. Akad. d. Wiss. Math.-Nat. Kl. (1982) 1-28.
10. Pohlers W. Subsytems of set theory and second order number theory, in: Buss S.R. (Ed.), Handbook of Proof Theory 1998 209-335 North-Holland Amsterdam
11. Rathjen M. Proof-theoretic analysis of KPM Arch. Math. Logic 30 1991 377-403
12. Richter W.H. Aczel P. Inductive definitions and reflecting properties of admissible ordinals, in: Fenstad J.E. Hinman P.G. (Eds.), Generalized Recursion Theory 1974 301-381 North-Holland Amsterdam
13. Takeuti G. A formalization of the theory of ordinal numbers J. Symbolic Logic 30 1965 295-317
14. Takeuti G. Proof Theory 2nd Edition 1987 North-Holland Amsterdam