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Formally self-referential propositions for cut free classical analysis and related systems

100%
Kreisel G., Takeuti G.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction............................................................................................................................................................................................................ 5   I. Results on self-referential propositions............................................................................................................................. 11     1. Definitions of some principal metamathematical notions................................................................... 11     2. Results concerning the notions of Section 1 for cut free classical     analysis and related systems........................................................................................................................ 16   II. Formalized metamathematics of C F A.............................................................................................................................. 24     1. Completeness and reflection principles for closed $∑^0_0$ ∪ $∑^0_q$ formulae..................... 24     2. Demonstrable instances of the normal form theorem......................................................................... 28     3. Demonstrable instances of deductive equivalence and of the fundamental conjecture............... 32   III. Discussion of some general issues raised in the introduction................................................................................... 34     1. Hilbert's programme.................................................................................................................................... 34     2. C F A and the structure of proofs in analysis.......................................................................................... 36     3. Henkin's problem [6] and the relation of synonymity............................................................................. 41   Appendix. Addenda to the literature......................................................................................................................................... 44     1. Jeroslow's variant of literal Gödel sentences......................................................................................... 44     2. Löb's theorem............................................................................................................................................... 44     3. Rosser variants............................................................................................................................................ 46   References.................................................................................................................................................................................. 49
2
Content available remote

Some applications of formalized consistency proofs

56%
Kreisel G., Wang H.
Fundamenta Mathematicae
|
1955
|
tom 42
|
nr 1
101-110
3
Content available remote

On the concepts of completeness and interpretation of formal systems

56%
Kreisel G.
Fundamenta Mathematicae
|
1952
|
tom 39
|
nr 1
103-127
4
Content available remote

Note on arithmetic models for consistent formulae of the predicate calculus

56%
Kreisel G.
Fundamenta Mathematicae
|
1950
|
tom 37
|
nr 1
265-285
5
Content available remote

Applications of formalized consistency proofs II

47%
Kreisel G., Wang H.
Fundamenta Mathematicae
|
1958
|
tom 45
|
nr 1
334-335
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