Cargando…
Varieties of constructive mathematics /
This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included w...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1987.
|
| Colección: | London Mathematical Society lecture note series ;
97. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Preface; Contents; 1. Foundations of Constructive Mathematics; 1. Existence and omniscience; 2. Basic constructions; 3. Informal intuitionistic logic; 4. Choice axioms; 5. Seal numbers; Problems; Notes; 2. Constructive Analysis; 1. Complete metric spaces; 2. Baire's theorem revisited; 3. Located subsets; 4. Totally Bounded Spaces; 5. Bounded Linear Maps; 6. Compactly Generated Banach Spaces; Problems; Notes; 3. Russian Constructive Mathematics; 1. Programming Systems and Omniscience Principles; 2. Continuity and intermediate values; 3. Specker's Sequence
- 4. The Helne-Borel Theorem5. Moduli of continuity and cozero sets; 6. Ceitin's theorem; Problems; Notes; 4. Constructive Algebra; 1. General considerations; 2. Factoring; 3. Splitting fields; 4. Uniqueness of splitting fields; 5. Finitely presented modules; 6. Noetherian rings; Problems; Notes; 5. Intuitionism; 1. Sequence spaces; 2. Continuous choice; 3. Uniform continuity; 4. The creating subject and Markov's principle; Problems; Notes; 6. Contrasting Varieties; 1. The Three Varieties; 2. Positive-valued Continuous Functions; Problems; Notes; 7. Intuitionistic Logic and Topos Theory
- 1. Intuitionistic prepositional calculus2. Predicate calculus; 3. The sheaf model C(X); 4. Presheaf topos models; Problems; Notes; Index