Logic and structure:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2013
|
| Edition: | 5. ed. |
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 263 S. graph. Darst. |
| ISBN: | 9781447145578 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Logic and structure
Autor: Dalen, Dirk van
Jahr: 2013
Contents
1 Introduction................................ 1
2 Prepositional Logic............................ 5
2.1 Propositions and Connectives.................... 5
2.2 Semantics .............................. 15
2.3 Some Properties of Prepositional Logic............... 20
2.4 Natural Deduction.......................... 29
2.5 Completeness............................ 38
2.6 The Missing Connectives...................... 46
3 Predicate Logic.............................. 53
3.1 Quantifiers.............................. 53
3.2 Structures .............................. 54
3.3 The Language of a Similarity Type................. 56
3.4 Semantics .............................. 64
3.5 Simple Properties of Predicate Logic................ 68
3.6 Identity................................ 77
3.7 Examples............................... 78
3.8 Natural Deduction.......................... 86
3.9 Adding the Existential Quantifier.................. 91
3.10 Natural Deduction and Identity................... 93
4 Completeness and Applications..................... 97
4.1 The Completeness Theorem..................... 97
4.2 Compactness and Skolem-Lowenheim............... 104
4.3 Some Model Theory......................... 1ll
4.4 Skolem Functions or How to Enrich Your Language........ 127
4.5 Ultraproducts............................. 134
5 Second-Order Logic........................... 145
6 Intuitionistic Logic............................ 155
6.1 Constructive Reasoning....................... 155
6.2 Intuitionistic Propositional and Predicate Logic...........157
6.3 Kripke Semantics..........................164
6.4 Some Model Theory.........................174
7 Normalization...............................187
7.1 Cuts ................................. 187
7.2 Normalization for Classical Logic.................. 191
7.3 Normalization for Intuitionistic Logic................ 197
7.4 Additional Remarks: Strong Normalization and the Church-
Rosser Property...........................207
8 Godel s Theorem.............................209
8.1 Primitive Recursive Functions.................... 209
8.2 Partial Recursive Functions..................... 218
8.3 Recursively Enumerable Sets.................... 229
8.4 Some Arithmetic........................... 236
8.5 Representability........................... 242
8.6 Derivability ............................. 245
8.7 Incompleteness............................ 250
References...................................257
Index......................................259
|
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| discipline | Mathematik |
| edition | 5. ed. |
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| indexdate | 2024-07-10T00:32:27Z |
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| isbn | 9781447145578 |
| language | English |
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| publishDateSort | 2013 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Dalen, Dirk van 1932- (DE-588)133205053 aut Logic and structure Dirk van Dalen 5. ed. London [u.a.] Springer 2013 X, 263 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Mathematische Logik (DE-588)4037951-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025701017&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dalen, Dirk van 1932- Logic and structure Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4123623-3 |
| title | Logic and structure |
| title_auth | Logic and structure |
| title_exact_search | Logic and structure |
| title_full | Logic and structure Dirk van Dalen |
| title_fullStr | Logic and structure Dirk van Dalen |
| title_full_unstemmed | Logic and structure Dirk van Dalen |
| title_short | Logic and structure |
| title_sort | logic and structure |
| topic | Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Mathematische Logik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025701017&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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