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...
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1987.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
97. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines. |
| Beschreibung: | 1 online resource (x, 149 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107361331 1107361338 |
| ISSN: | 0076-0052 ; |
Internformat
MARC
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| 245 | 1 | 0 | |a Varieties of constructive mathematics / |c Douglas Bridges, Fred Richman. |
| 260 | |a Cambridge [Cambridgeshire] ; |a New York : |b Cambridge University Press, |c 1987. | ||
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| 490 | 1 | |a London Mathematical Society lecture note series, |x 0076-0052 ; |v 97 | |
| 504 | |a Includes bibliographical references and index. | ||
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| 520 | |a 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 where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 1. Intuitionistic prepositional calculus2. Predicate calculus; 3. The sheaf model C(X); 4. Presheaf topos models; Problems; Notes; Index | |
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| _version_ | 1813903607533142016 |
| adam_text | |
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| author | Bridges, D. S. (Douglas S.), 1945- |
| author2 | Richman, Fred, 1938- |
| author2_role | |
| author2_variant | f r fr |
| author_GND | http://id.loc.gov/authorities/names/n79042781 http://id.loc.gov/authorities/names/n50044714 |
| author_facet | Bridges, D. S. (Douglas S.), 1945- Richman, Fred, 1938- |
| author_role | |
| author_sort | Bridges, D. S. 1945- |
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| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.56 .B75 1987eb |
| callnumber-search | QA9.56 .B75 1987eb |
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| callnumber-subject | QA - Mathematics |
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| contents | 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 |
| ctrlnum | (OCoLC)839527997 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839527997 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:22Z |
| institution | BVB |
| isbn | 9781107361331 1107361338 |
| issn | 0076-0052 ; |
| language | English |
| oclc_num | 839527997 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (x, 149 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series, |
| spelling | Bridges, D. S. (Douglas S.), 1945- https://id.oclc.org/worldcat/entity/E39PBJdx4j3VyWckKGVhJyTGpP http://id.loc.gov/authorities/names/n79042781 Varieties of constructive mathematics / Douglas Bridges, Fred Richman. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987. 1 online resource (x, 149 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series, 0076-0052 ; 97 Includes bibliographical references and index. Print version record. 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 where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines. 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 Constructive mathematics. http://id.loc.gov/authorities/subjects/sh85031452 Mathématiques constructives. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Constructive mathematics fast Konstruktive Mathematik gnd http://d-nb.info/gnd/4165105-4 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Sistemas lógicos não clássicos. larpcal Matemática construtiva. larpcal Mathématiques constructives. ram Logique symbolique et mathématique. ram Richman, Fred, 1938- https://id.oclc.org/worldcat/entity/E39PBJrgDCVkTdKwdmVW3XgBT3 http://id.loc.gov/authorities/names/n50044714 Print version: Bridges, D.S. (Douglas S.), 1945- Varieties of constructive mathematics. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987 0521318025 (DLC) 85026904 (OCoLC)12808271 London Mathematical Society lecture note series ; 97. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552387 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552387 Volltext |
| spellingShingle | Bridges, D. S. (Douglas S.), 1945- Varieties of constructive mathematics / London Mathematical Society lecture note series ; 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 Constructive mathematics. http://id.loc.gov/authorities/subjects/sh85031452 Mathématiques constructives. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Constructive mathematics fast Konstruktive Mathematik gnd http://d-nb.info/gnd/4165105-4 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Sistemas lógicos não clássicos. larpcal Matemática construtiva. larpcal Mathématiques constructives. ram Logique symbolique et mathématique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031452 http://d-nb.info/gnd/4165105-4 http://d-nb.info/gnd/4037951-6 |
| title | Varieties of constructive mathematics / |
| title_auth | Varieties of constructive mathematics / |
| title_exact_search | Varieties of constructive mathematics / |
| title_full | Varieties of constructive mathematics / Douglas Bridges, Fred Richman. |
| title_fullStr | Varieties of constructive mathematics / Douglas Bridges, Fred Richman. |
| title_full_unstemmed | Varieties of constructive mathematics / Douglas Bridges, Fred Richman. |
| title_short | Varieties of constructive mathematics / |
| title_sort | varieties of constructive mathematics |
| topic | Constructive mathematics. http://id.loc.gov/authorities/subjects/sh85031452 Mathématiques constructives. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Constructive mathematics fast Konstruktive Mathematik gnd http://d-nb.info/gnd/4165105-4 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Sistemas lógicos não clássicos. larpcal Matemática construtiva. larpcal Mathématiques constructives. ram Logique symbolique et mathématique. ram |
| topic_facet | Constructive mathematics. Mathématiques constructives. MATHEMATICS Infinity. MATHEMATICS Logic. Constructive mathematics Konstruktive Mathematik Mathematische Logik Sistemas lógicos não clássicos. Matemática construtiva. Logique symbolique et mathématique. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552387 |
| work_keys_str_mv | AT bridgesds varietiesofconstructivemathematics AT richmanfred varietiesofconstructivemathematics |