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Constructivism in mathematics : an introduction. Volume 1 /
Constructivism in Mathematics Vol.1.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
North-Holland,
1988.
|
| Colección: | Studies in logic and the foundations of mathematics ;
v. 121. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Constructivism in Mathematics: An Introduction; Copyright Page; CONTENTS OF VOLUME I; Preface; Preliminaries; Chapter 1 Introduction; 1. Constructivism; 2. Constructivity; 3. Weak counterexamples; 4. A brief history of constructivism; 5. Notes; Exercises; Chapter 2 Logic; 1. Natural deduction; 2. Logic with existence predicate; 3. Relationships between classical and intuitionistic logic; 4. Hilbert-type systems; 5. Kripke semantics; 6. Completeness for Kripke semantics; 7. Definitional extensions; 8. Notes; Exercises; Chapter 3 Arithmetic
- 1. Informal arithmetic and primitive recursive functions2. Primitive recursive arithmetic PRA; 3. Intuitionistic first-order arithmetic HA; 4. Algorithms; 5. Some metamathematics of HA; 6. Elementary analysis and elementary inductive definitions; 7. Formalization of elementary recursion theory; 8. Intuitionistic second-order logic and arithmetic; 9. Higher-order logic and arithmetic; 10. Notes; Exercises; Chapter 4 Non-classical axioms; 1. Preliminaries; 2. Choice axioms; 3. Church's thesis; 4. Realizability; 5. Markov's principle; 6. Choice sequences and continuity axioms; 7. The fan theorem
- 8. Bar induction and generalized inductive definitions9. Uniformity principles and Kripke's schema; 10. Notes; Exercises; Chapter 5 Real numbers; 1. Introduction; 2. Cauchy reals and their ordering; 3. Arithmetic on R; 4. Completeness properties and relativization; 5. Dedekind reals; 6. Arithmetic of Dedekind reals and extended reals; 7. Two metamathematical digressions; 8. Notes; Exercises; Chapter 6 Some elementary analysis; 1. Intermediate-value and supremum theorems; 2. Differentiation and integration; 3. Consequences of WC-N and FAN; 4. Analysis in CRM: consequences of CT0, ECT0, MP
- 5. NotesExercises; Bibliography; Index; List of symbols