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
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