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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

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

First order topology

82%

Henson C. W., Jockusch, Jr. C. G., Rubel L. A., Takeuti G.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS § 1. Introduction.................................................................................................... 5 § 2. Basic development............................................................................................... 8 § 3. Some elementarily equivalent spaces............................................................. 11 § 4. Elementary characterizations of some familiar spaces................................ 13 § 5. First order properties of C(X).............................................................................. 16 § 6. ℒ(X) and C(X) compared..................................................................................... 26 § 7. Some results on undecidability.......................................................................... 28 § 8. The class of topology lattices............................................................................. 32 § 9. Some bounds on the Löwenheim number for topology lattices.................. 33 §10. Open questions................................................................................................... 36 References.................................................................................................................... 39

Ograniczanie wyników

2 Takeuti G.

1 Henson C. W.

1 Jockusch, Jr. C. G.

1 Kreisel G.

1 Rubel L. A.

1 1977

1 1974

Wyniki wyszukiwania

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

First order topology