Książka - szczegóły

CONTENTS
Introduction..............................................................................................................................................5
I. Naive set theory.....................................................................................................................................6
1. The formal system................................................................................................................................6
2. Inversion and reduction properties of the rules of inference..............................................................12
3. Rules of contraction...........................................................................................................................17
4. Normalizability.....................................................................................................................................22
5. Counter-examples to normalizability in set theory...............................................................................24
6. C-normalizability.................................................................................................................................28
7. Concepts of normalizability and C-normalizability for naive set theory with intuitionistic logic.............33
II. Well-founded fragments of naive set theory........................................................................................33
1. Basic definitions, properties of C-normal deductions..........................................................................33
2. Axioms for set theory..........................................................................................................................37
3. The language SET..............................................................................................................................50
4. Semantical motivation for the rules of contraction..............................................................................54
III. C-normalizability of deductions in well-founded fragments of naive set theory...................................62
1. Well-foundedness predicates and well-foundedness objects.............................................................63
2. $ϕ_{T(x̅)}(α̅(t̅))$..................................................................................................................................66
3. The substitution property....................................................................................................................84
4. Every deduction in N satisfies some negation closed W-predicate.....................................................87
5. C-normalizability for well-founded fragments of naive set theory with intuitionistic logic.....................92
6. Notes..................................................................................................................................................94
References.............................................................................................................................................95