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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
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 -
