Książka - szczegóły

CONTENTS

Introduction............................................................................................................ 5

A. The three-valued predicate calculus............................................................ 8
 A 1. Three-valued structures; classical case............................................. 8
 A 2. Three-valued structures; intuitionistic case........................................ 10
 A 3. Theories; models..................................................................................... 12
 A 4. The completeness theorem.................................................................. 14
 A 5. The thinness theorem............................................................................. 18
B. Three-valued analysis and cut elimination......................................................... 19
 B 1. The syntax................................................................................................. 19
 B 2. The semantics......................................................................................... 22
 B 3. Cut-free provability................................................................................... 23
 B 4. Takeuti's conjecture................................................................................ 28
C. Applications to the metamathematics of cut-free analysis.............................. 30
 C 1. Poor and absorbing formulas............................................................... 31
 C 2. A candidate for synonymity.................................................................... 32
 C 3. Syntactic conditions for poverty............................................................. 35
 C 4. Takeuti's conjectures and $∑^0_1$-reflection.................................. 36
 C 5. Cut elimination in the classical case.................................................. 37
 C 6. The poverty theorem............................................................................... 39
Appendix......................................................................................................................... 41
 1. Tait's proof.................................................................................................... 41
 2. Prawitz's proof.............................................................................................. 42
 3. Prawitz's third proof..................................................................................... 43
 4. The co-rule.................................................................................................... 43
 5. The simple theory of types......................................................................... 44

 References............................................................................................... 45