Semantical investigations in Heyting's intuitionistic logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Reidel
1981
|
| Series: | Synthese library.
148. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 287 S. |
| ISBN: | 9027712026 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Titel: Semantical investigations in Heyting s intuitionistic logic
Autor: Gabbay, Dov M.
Jahr: 1981
TABLE OF CONTENTS
PREFACE V
INTRODUCTION 1
chapter 1 / Logical Systems and Semantics 6
1. Scott and Tarski Systems 6
2. Scott Semantics 1 10
3. What is a Classical Connective? 12
4. Scott Semantics 2 17
Notes 19
chapter 2 / Introducing HPC 20
1. Heyting s Implication 20
2. Heyting s Predicate Logic (HPC) 26
3. The Disjunction and Existence Properties 30
4. Heyting s Negation 35
5. Classical Predicate Calculus (CPC) 37
6. The System CD 40
7. The System MH* 41
Notes 42
chapter 3 / The Kripke, Beth and Topological
Interpretations for HPC 43
1. Kripke Structures 43
2. Beth Interpretation 47
3. Structures with Constant Domains 50
4. Kripke Interpretation for MH 57
5. Topological Interpretation 59
Notes 62
chapter 4 / Heyting s Propositional Calculus and
Extensions 63
1. h and c 63
2. Filtration 69
3. Incomparable Intermediate Logics 73
4. The Fragment without v 76
Notes 82
vii
viii TABLE OF CONTENTS
chapter 5 / Three Intermediate Logics 83
1. The Logic of Finite n-ary Trees 83
2. The Kreisel-Putnam System 95
3. An Intermediate Logic without f.m.p. 103
4. Exercises 105
Notes 107
chapter 6 / Formulas in One Variable 108
1. Nishimura Lattice 108
2. The Disjunction Property for yn 115
Note 120
chapter 7 / Propositional Connectives 121
1. Negation 121
2. Strong Negation 124
3. Functional Completeness 127
4. New Intuitionistic Connectives 130
5. Modality 140
Notes 144
chapter 8 / The Interpolation Theorem 145
1. General Consistency Theorem 145
2. Robinson s Theorem 146
3. Craig s Theorem 153
Notes 158
chapter 9 / Second Order Propositional Calculus 159
1. The System 2ft 159
2. The Completeness Theorem 160
3. Examples of Connectives in 2h 165
Notes 169
chapter 10 / Modified Kripke Interpretation 170
1. Theory of Equality 170
2. Function Symbols and = 171
3. Some Model Theory 173
Note 177
chapter 11 / Theories in HPC 1 178
1. Some Intuitionistic Theories 179
2. Some General Theorems 181
3. End Extensions 186
TABLE OF CONTENTS ix
chapter 12 / Theories in HPC 2 193
1. Equality 193
2. The Apartness Relation 194
3. Linear Order 194
4. One Unary Function 196
5. Groups 197
6. Fields 199
7. A Fragment of Arithmetic 200
Note 202
chapter 13 / Completeness of HPC with Respect to RE and
Post Structures 203
1. The Results 204
2. Positive Results 204
3. Negative Results 218
4. Tarski s Interpretation for HPC as a Calculus of Systems 220
5. Kreisel s Notion of Validity in Post Systems 221
6. Weak Validity in Post Systems 224
7. Validity in Post Systems 225
Notes 226
chapter 14 / Undecidability Results 227
1. General Theorems 227
2. Undecidability Results 234
3. Undecidability of Classically Model Complete Theories 237
4. Undecidability of Theories Formulated with the Apartness
Relation 245
5. Undecidability of Some Finite Extensions of the Theory of
Abelian Groups 258
6. Undecidability of the Second Order Propositional
Calculus 262
Notes 265
chapter 15 / Decidability Results 266
1. Decided Monadic Predicates 267
2. Unary Functions with Decided Equality 269
3. Monadic Fragment Again 272
4. Some Abelian Groups 277
5. Linear Order 279
Notes 279
X TABLE OF CONTENTS
REFERENCES 280
INDEX 285
|
| any_adam_object | 1 |
| author | Gabbay, Dov M. 1945- |
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| dewey-full | 511/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.2 |
| dewey-search | 511/.2 |
| dewey-sort | 3511 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
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| indexdate | 2024-07-09T15:43:37Z |
| institution | BVB |
| isbn | 9027712026 |
| language | English |
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| publishDate | 1981 |
| publishDateSearch | 1981 |
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| publisher | Reidel |
| record_format | marc |
| series | Synthese library. |
| series2 | Synthese library. |
| spelling | Gabbay, Dov M. 1945- Verfasser (DE-588)124196314 aut Semantical investigations in Heyting's intuitionistic logic Dordrecht u.a. Reidel 1981 X, 287 S. txt rdacontent n rdamedia nc rdacarrier Synthese library. 148. Heyting, A <1898-> (Arend) Intuïtionisme gtt Wiskundige logica gtt Intuitionistic mathematics Semantik (DE-588)4054490-4 gnd rswk-swf Intuitionistische Logik (DE-588)4162199-2 gnd rswk-swf Intuitionistische Logik (DE-588)4162199-2 s Semantik (DE-588)4054490-4 s DE-604 Synthese library. 148. (DE-604)BV000005044 148. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001511080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gabbay, Dov M. 1945- Semantical investigations in Heyting's intuitionistic logic Synthese library. Heyting, A <1898-> (Arend) Intuïtionisme gtt Wiskundige logica gtt Intuitionistic mathematics Semantik (DE-588)4054490-4 gnd Intuitionistische Logik (DE-588)4162199-2 gnd |
| subject_GND | (DE-588)4054490-4 (DE-588)4162199-2 |
| title | Semantical investigations in Heyting's intuitionistic logic |
| title_auth | Semantical investigations in Heyting's intuitionistic logic |
| title_exact_search | Semantical investigations in Heyting's intuitionistic logic |
| title_full | Semantical investigations in Heyting's intuitionistic logic |
| title_fullStr | Semantical investigations in Heyting's intuitionistic logic |
| title_full_unstemmed | Semantical investigations in Heyting's intuitionistic logic |
| title_short | Semantical investigations in Heyting's intuitionistic logic |
| title_sort | semantical investigations in heyting s intuitionistic logic |
| topic | Heyting, A <1898-> (Arend) Intuïtionisme gtt Wiskundige logica gtt Intuitionistic mathematics Semantik (DE-588)4054490-4 gnd Intuitionistische Logik (DE-588)4162199-2 gnd |
| topic_facet | Heyting, A <1898-> (Arend) Intuïtionisme Wiskundige logica Intuitionistic mathematics Semantik Intuitionistische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001511080&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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