Abstract:
This paper deals with the proof theory of rst order applicative theories with non-constructive operator and a form of the bar rule, yielding systems of ordinal strength 0 and '20, respectively. Relevant use is made of xed point theories with ordinals plus bar rule.
Citations
|
71
|
A language and axioms for explicit mathematics
– Feferman
- 1975
|
|
59
|
Constructive theories of functions and classes
– Feferman
- 1979
|
|
55
|
Proof theory: Some applications of cut-elimination
– Schwichtenberg
- 1977
|
|
44
|
Foundations of constructive mathematics. Metamathematical studies, volume 6 of Ergebnisse der Mathematik und ihrer Grenzgebiete
– Beeson
- 1985
|
|
38
|
Systems of explicit mathematics with non-constructive ยต-operator
– Feferman, ager, et al.
- 1993
|
|
35
|
Proof Theory: An Introduction
– Pohlers
- 1989
|
|
31
|
Systems of predicative analysis
– Feferman
- 1964
|
|
11
|
Fixed points in Peano arithmetic with ordinals
– ager, G
- 1993
|
|
10
|
Proof Theory
– utte, K
- 1977
|
|
8
|
Systems of explicit mathematics with nonconstructive -operator and join. Annals of Pure and Applied Logic
– Gla, Strahm
- 1996
|
|
7
|
Totality in applicative theories
– ager, G, et al.
- 1995
|
|
6
|
order theories with ordinals and elementary comprehension
– ager, G, et al.
- 1995
|
|
4
|
Some theories with positive induction of ordinal strength '!0
– ager, G, et al.
- 1996
|
|
3
|
Theories for Admissible Sets: A Unifying Approach to Proof Theory
– AGER
- 1986
|
|
2
|
A note on a predicatively reducible theory of iterated elementary induction
– Cantini
- 1985
|
|
1
|
Autonomous trans progressions and the extent of predicative mathematics
– Feferman
- 1968
|
|
1
|
Formal theories for trans iteration of generalized inductive de and some subsystems of analysis
– Feferman
- 1968
|
|
1
|
Choice principles, the bar rule and autonomoulsy iterated comprehension schemes in analysis
– Feferman, ager, et al.
- 1982
|
|
1
|
The unfolding of non- arithmetic. Annals of Pure and Applied Logic
– Feferman, Strahm
|
|
1
|
Iterated inductive de and 2 -AC
– Friedman
- 1968
|
|
1
|
The quanti operator in explicit mathematics with universes and iterated point theories with ordinals. Archive for Mathematical Logic 37
– Marzetta, Strahm
- 1998
|
|
1
|
A theory of rules for enumerated classes of functions. Archive for Mathematical Logic 34
– uter, A
- 1995
|