Chapter IV Subsystems of set theory and second order number theory

Studies in Logic and the Foundations of Mathematics

Volumn 137, Issue C, 1998, Pages 209-335

  Pohlers, Wolfram ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956693883     PISSN: 0049237X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0049-237X(98)80019-0     Document Type: Chapter

References (45)

1. In: Aczel P.H.G., Simmons H., and Wainer S.S. (Eds). Proof Theory July (1992), Cambridge University Press, Cambridge
2. Barwise J. Admissible Sets and Structures. Perspectives in Mathematical Logic (1975), Springer-Verlag, Berlin
3. To appear in. Beckmann A., and Pohlers W. Application of cut-free infinitary derivations to generalized recursion theory. Annals of Pure and Applied Logic (1997)
4. 0 -Skolem Funktionen. Dissertation (1997), Westfälische Wilhelms-Universität, Münster
5. Blankertz B., and Weiermann A. How to characterize provably total functions by the Buchholz' operator method. In: Hájek P. (Ed). Gödel '96: Logical Foundations of Mathematics, Computer Science and Physics-Kurt Gödel's Legacy. Lecture Notes in Logic #6 (1996), Springer-Verlag, Berlin 205-213
6. Buchholz W. Notation systems for infinitary derivations. Archive for Mathematical Logic 30 (1991) 277-296
7. W. Buchholz [1992] A simplified version of local predicativity, in: Aczel, Simmons and Wainer [1992], pp. 115-147.
8. Buchholz W., Cichon E.A., and Weiermann A. A uniform approach to fundamental sequences and hierarchies. Mathematical Logic Quarterly 40 (1994) 273-286
9. In: Buchholz W., Feferman S., Pohlers W., and Sieg W. (Eds). Interated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies. Lecture Notes in Mathematics #897 (1981), Springer-Verlag, Berlin
10. Buchholz W., and Pohlers W. Provable well orderings of formal theories for transfinitely iterated inductive definitions. Journal of Symbolic Logic 43 (1978) 118-125
11. Feferman S. Systems of predicative analysis. Journal of Symbolic Logic 29 (1964) 1-30
12. S. Feferman [1970] Formal theories for transfinite iteration of generalized inductive definitions and some subsystems of analysis, in: Kino, Myhill and Vesley [1970], pp. 303-326.
13. H. M. Friedman [1970] Iterated inductive definitions and Σ1/2-AC, in: Kino, Myhill and Vesley [1970], pp. 435-442.
14. Friedman H.M., and Sheard M. Elementary descent recursion and proof theory. Annals of Pure and Applied Logic 71 (1995) 1-45
15. Girard J.-Y. Proof Theory and Logical Complexity vol. 1 (1987), Bibliopolis, Naples
16. Jäger G. Theories for iterated jumps. Handwritten notes (1980)
17. Jäger G. Theories for Admissible Sets. A Unifying Approach to Proof Theory. Studies in Proof Theory, Lecture Notes, #2 (1986), Bibliopolis, Naples
18. G. Jäger, R. Kahle, A. Setzer, and T. Strahm [n.d.] The proof-theoretic analysis of transfinitely iterated fixed point theories. To appear in Journal of Symbolic Logic.
19. Jäger G., and Pohlers W. Eine beweistheoretische Untersuchung von (Δ1/2-CA)+(BI) und verwandter Systeme. Bayerische Akademie der Wissenschaften, Sitzungsberichte 1982 (1983) 1-28
20. G. Jäger and T. Strahm [n.d.] Fixed point theories and dependent choice. Submitted for publication.
21. Kahle R. Applicative Theories and Frege Structures. Dissertation (1997), Institut für Informatik und angewandte Mathematik, Universität Bern, Bern
22. In: Kino A., Myhill J., and Vesley R.E. (Eds). Intuitionism and Proof Theory. Studies in Logic and the Foundations of Mathematics (1970), North-Holland, Amsterdam
23. Moschovakis Y.N. Elementary Induction on Abstract Structures. Studies in Logic and the Foundations of Mathematics #77 (1974), North-Holland, Amsterdam
24. E. Palmgren [n.d.] On universes in type theory. To appear.
25. Platek R. Foundations of Recursion Theory II. dissertation (1966), Stanford University
26. Pohlers W. Ordinals connected with formal theories for transfinitely iterated inductive definitions. Journal of Symbolic Logic 43 (1978) 161-182
27. v by the method of local predicativity, in: Buchholz et al. [1981], pp. 261-357.
28. Pohlers W. Admissibility in proof theory; a survey. In: Cohen L.J., L{middle dot}os J., Pfeiffer H., and Podewski K.-P. (Eds). Logic, Methodology and Philosophy of Science VI. Studies in Logic and the Foundations of Mathematics #104 (1982), North-Holland, Amsterdam, Aug. 123-139
29. Pohlers W. Cut elimination for impredicative infinitary systems II. Ordinal analysis for iterated inductive definitions. Archiv für Mathematische Logik und Grundlagenforschung 22 (1982) 69-87
30. Pohlers W. Proof Theory. An Introduction. Lecture Notes in Mathematics #1407 (1989), Springer-Verlag, Berlin
31. Pohlers W. Proof theory and ordinal analysis. Archive for Mathematical Logic 30 (1991) 311-376
32. W. Pohlers [1992] A short course in ordinal analysis, in: Aczel, Simmons and Wainer [1992], pp. 27-78.
33. Rathjen M. Untersuchungen zu Teilsystemen der Zahlentheorie zweiter Stufe und der Mengenlehre mit einer zwischen Δ1/2-CA und Δ1/2-CA+BI liegenden Beweisstärke. Dissertation (1988), Westfälische Wilhelms-Universität, Münster
34. Rathjen M. The role of parameters in bar rule and bar induction. Journal of Symbolic Logic 56 (1991) 715-730
35. Rathjen M. Recent advances in ordinal analysis: Π1/2-CA and related systems. Bulletin of Symbolic Logic 1 (1995) 468-485
36. A. Schlüter [n.d.] What is provable using first order reflection. To appear in Annal of Pure and Applied Logic.
37. Schlüter A. Autonom erreichbare Mengen. Diplomarbeit (1990), Westfälische Wilhelms-Universität, Münster
38. Schlüter A. Zur Mengenexistenz in formalen Theorien der Mengenlehre. Dissertation (1993), Westfälische Wilhelms-Universität, Münster
39. Translated into English as Schütte [1977]. Schütte K. Beweistheorie (1960), Springer-Verlag, Berlin
40. Schütte K. Eine Grenze für die Beweisbarkeit der transfiniten Induktion in der verzweigten Typenlogik. Archiv für Mathematische Logik und Grundlagenforschung 7 (1965) 45-60
41. Schütte K. Predicative well-orderings. In: Crossley J.N., and Dummett M.A.E. (Eds). Formal Systems and Recursive Functions. Studies in Logic and the Foundations of Mathematics July (1965), North-Holland, Amsterdam 280-303
42. Schütte K. Proof Theory (1977), Springer-Verlag, Berlin
43. T. Strahm [n.d.] First steps into metapredicativity in explicit mathematics. In preparation.
44. Takeuti G. Proof Theory (1975), North-Holland, Amsterdam
45. Weiermann A. How to characterize provably total functions by local predicativity. Journal of Symbolic Logic 61 (1996) 52-69