CONTENTSIntroduction............................................................................................................................................................................................................ 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 ∪ 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
@book{bwmeta1.element.zamlynska-23b1447d-c2c3-4004-849e-d24eec516eb8,
author = {G. Kreisel and G. Takeuti},
title = {Formally self-referential propositions for cut free classical analysis and related systems},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1974},
zbl = {0336.02027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-23b1447d-c2c3-4004-849e-d24eec516eb8}
}
G. Kreisel; G. Takeuti. Formally self-referential propositions for cut free classical analysis and related systems. GDML_Books (1974), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-23b1447d-c2c3-4004-849e-d24eec516eb8/