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

G. Kreisel, and G. Takeuti. Formally self-referential propositions for cut free classical analysis and related systems. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1974. <http://eudml.org/doc/268467>.

@book{G1974,
abstract = {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 $∑^0_0$ ∪ $∑^0_q$ 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},
author = {G. Kreisel, G. Takeuti},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Formally self-referential propositions for cut free classical analysis and related systems},
url = {http://eudml.org/doc/268467},
year = {1974},
}

TY - BOOK
AU - G. Kreisel
AU - G. Takeuti
TI - Formally self-referential propositions for cut free classical analysis and related systems
PY - 1974
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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 $∑^0_0$ ∪ $∑^0_q$ 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
LA - eng
UR - http://eudml.org/doc/268467
ER -