Mathematical intuitionism: introduction to proof theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1988
|
| Schriftenreihe: | Translations of mathematical monographs
67 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | EST: Matematičeskij intuicionizm <engl.>. - Aus d. Russ. übers. |
| Beschreibung: | IX, 228 S. |
| ISBN: | 0821845209 |
Internformat
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| 100 | 1 | |a Dragalin, Alb́ert G. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Matematičeskij intuicionizm |
| 245 | 1 | 0 | |a Mathematical intuitionism |b introduction to proof theory |c A. G. Dragalin |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1988 | |
| 300 | |a IX, 228 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 67 | |
| 500 | |a EST: Matematičeskij intuicionizm <engl.>. - Aus d. Russ. übers. | ||
| 650 | 7 | |a Logica Matematica |2 larpcal | |
| 650 | 4 | |a Logique symbolique et mathématique | |
| 650 | 4 | |a Intuitionistic mathematics | |
| 650 | 0 | 7 | |a Intuitionistische Mathematik |0 (DE-588)4162200-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804115305688989696 |
|---|---|
| adam_text | Contents
Preface vii
Part 1. Logic 1
§1. Informal explanations 1
§2. Intuitionistic predicate logic 7
§3. The sequent calculus 10
§4. Some results on intuitionistic predicate logic 15
§5. The classical sequent calculus 17
§6. Formal axiomatic theories 19
§7. Bibliographic remarks 20
Part 2. Arithmetic 23
§1. The analytic language 23
§2. Basic arithmetic theories 26
§3. The negative interpretation 30
§4. The formal thesis of Church 33
§5. Recursive readability in Kleene s sense 36
§6. Recursive realizability and effectiveness properties of the logical
connectives in HA 43
§7. The principle of constructive choice (Markov s principle) and
principle P 44
§8. Additional results 49
§9. The semantics of realizability for predicate logic 54
§10. Additional bibliographic remarks 56
Part 3. Algebraic Models 59
§1. Pseudo Boolean algebras, topological spaces 59
§2. Completion algebras, Beth Kripke frames 69
§3. Applications to propositional logic. Intuitionistic logic is not
finite valued 76
§4. Beth Kripke models; algebraic and topological models 79
V
vi CONTENTS
§5. Completeness theorems 97
§6. Applications to intuitionistic arithmetic; the Smoryriski operator 114
§7. The readability method and the theory of intuitionistic models 118
§8. De Jongh semantics 123
§9. Additional bibliographic remarks 124
Part 4. Analysis 125
§1. The theory FIM: a survey of results 125
§2. The Kripke scheme 132
§3. The theory IDB(f/) 137
§4. The theory of CS 140
§5. The theory LS of lawless sequences 142
§6. Examples of models 145
Part 5. Eliminability of Cuts in the Intuitionistic Simple Theory of
Types in the Form of a Sequent Calculus with Extensionality 153
Appendix A. An Algebraic Approach to Models of Realizability Type 173
Appendix B. A Strong Form of the Normalization Theorem 185
Bibliography 201
Indices 217
Index of Names 217
Subject Index 219
Names of formal theories 225
Names of axioms and rules of inference 226
Notation for formulas and terms 227
Realizabilities 228
|
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
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| id | DE-604.BV000851260 |
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| indexdate | 2024-07-09T15:20:30Z |
| institution | BVB |
| isbn | 0821845209 |
| language | English Russian |
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| physical | IX, 228 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | American Math. Soc. |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Dragalin, Alb́ert G. Verfasser aut Matematičeskij intuicionizm Mathematical intuitionism introduction to proof theory A. G. Dragalin Providence, RI American Math. Soc. 1988 IX, 228 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 67 EST: Matematičeskij intuicionizm <engl.>. - Aus d. Russ. übers. Logica Matematica larpcal Logique symbolique et mathématique Intuitionistic mathematics Intuitionistische Mathematik (DE-588)4162200-5 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s Intuitionistische Mathematik (DE-588)4162200-5 s DE-604 Translations of mathematical monographs 67 (DE-604)BV000002394 67 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000534462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dragalin, Alb́ert G. Mathematical intuitionism introduction to proof theory Translations of mathematical monographs Logica Matematica larpcal Logique symbolique et mathématique Intuitionistic mathematics Intuitionistische Mathematik (DE-588)4162200-5 gnd Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4162200-5 (DE-588)4145177-6 |
| title | Mathematical intuitionism introduction to proof theory |
| title_alt | Matematičeskij intuicionizm |
| title_auth | Mathematical intuitionism introduction to proof theory |
| title_exact_search | Mathematical intuitionism introduction to proof theory |
| title_full | Mathematical intuitionism introduction to proof theory A. G. Dragalin |
| title_fullStr | Mathematical intuitionism introduction to proof theory A. G. Dragalin |
| title_full_unstemmed | Mathematical intuitionism introduction to proof theory A. G. Dragalin |
| title_short | Mathematical intuitionism |
| title_sort | mathematical intuitionism introduction to proof theory |
| title_sub | introduction to proof theory |
| topic | Logica Matematica larpcal Logique symbolique et mathématique Intuitionistic mathematics Intuitionistische Mathematik (DE-588)4162200-5 gnd Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Logica Matematica Logique symbolique et mathématique Intuitionistic mathematics Intuitionistische Mathematik Beweistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000534462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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