The mathematics of logic: a guide to completeness theorems and their applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 204 S. graph. Darst. |
| ISBN: | 9780521708777 9780521882194 |
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MARC
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| 245 | 1 | 0 | |a The mathematics of logic |b a guide to completeness theorems and their applications |c Richard Kaye |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XI, 204 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
Preface page vii
How to read this book xii
1 König s Lemma 1
1.1 Two ways of looking at mathematics 1
1.2 Examples and exercises 6
1.3 König s Lemma and reverse mathematics* 9
2 Posets and maximal elements 11
2.1 Introduction to order 11
2.2 Examples and exercises 17
2.3 Zorn s Lemma and the Axiom of Choice* 20
3 Formal systems 24
3.1 Formal systems 24
3.2 Examples and exercises 33
3.3 Post systems and computability* 35
4 Deductions in posets 38
4.1 Proving statements about a poset 38
4.2 Examples and exercises 47
4.3 Linearly ordering algebraic structures* 49
5 Boolean algebras 55
5.1 Boolean algebras 55
5.2 Examples and exercises 61
5.3 Boolean algebra and the algebra of Boole* 61
6 Propositional logic 64
6.1 A system for proof about propositions 64
6.2 Examples and exercises 75
6.3 Decidability of propositional logic* 77
vi Contents
7 Valuations 80
7.1 Semantics for prepositional logic 80
7.2 Examples and exercises ¦ 90
7.3 The complexity of satisfiability* 95
8 Filters and ideals 100
8.1 Algebraic theory of boolean algebras 100
8.2 Examples and exercises 107
8.3 Tychonov s Theorem* 108
8.4 The Stone Representation Theorem* 110
9 First-order logic 116
9.1 First-order languages 116
9.2 Examples and exercises 134
9.3 Second-and higher-order logic* 137
10 Completeness and compactness 140
10.1 Proof of completeness and compactness 140
10.2 Examples and exercises 146
10.3 The Compactness Theorem and topology* 149
10.4 The Omitting Types Theorem* 152
11 Model theory 160
11.1 Countable models and beyond 160
11.2 Examples and exercises 173
11.3 Cardinal arithmetic* 176
12 Nonstandard analysis 182
12.1 Infinitesimal numbers 182
12.2 Examples and exercises 186
12.3 Overspill and applications* 187
References , 199
Index 200
|
| adam_txt |
Contents
Preface page vii
How to read this book xii
1 König's Lemma 1
1.1 Two ways of looking at mathematics 1
1.2 Examples and exercises 6
1.3 König's Lemma and reverse mathematics* 9
2 Posets and maximal elements 11
2.1 Introduction to order 11
2.2 Examples and exercises 17
2.3 Zorn's Lemma and the Axiom of Choice* 20
3 Formal systems 24
3.1 Formal systems 24
3.2 Examples and exercises 33
3.3 Post systems and computability* 35
4 Deductions in posets 38
4.1 Proving statements about a poset 38
4.2 Examples and exercises 47
4.3 Linearly ordering algebraic structures* 49
5 Boolean algebras 55
5.1 Boolean algebras 55
5.2 Examples and exercises 61
5.3 Boolean algebra and the algebra of Boole* 61
6 Propositional logic 64
6.1 A system for proof about propositions 64
6.2 Examples and exercises 75
6.3 Decidability of propositional logic* 77
vi Contents
7 Valuations 80
7.1 Semantics for prepositional logic 80
7.2 Examples and exercises ¦ 90
7.3 The complexity of satisfiability* 95
8 Filters and ideals 100
8.1 Algebraic theory of boolean algebras 100
8.2 Examples and exercises 107
8.3 Tychonov's Theorem* 108
8.4 The Stone Representation Theorem* 110
9 First-order logic 116
9.1 First-order languages 116
9.2 Examples and exercises 134
9.3 Second-and higher-order logic* 137
10 Completeness and compactness 140
10.1 Proof of completeness and compactness 140
10.2 Examples and exercises 146
10.3 The Compactness Theorem and topology* 149
10.4 The Omitting Types Theorem* 152
11 Model theory ' ' ' 160
11.1 Countable models and beyond 160
11.2 Examples and exercises 173
11.3 Cardinal arithmetic* 176
12 Nonstandard analysis 182
12.1 Infinitesimal numbers 182
12.2 Examples and exercises 186
12.3 Overspill and applications* 187
References , 199
Index 200 |
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| isbn | 9780521708777 9780521882194 |
| language | English |
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| spelling | Kaye, Richard Verfasser aut The mathematics of logic a guide to completeness theorems and their applications Richard Kaye 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XI, 204 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf 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=015990279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaye, Richard The mathematics of logic a guide to completeness theorems and their applications Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | The mathematics of logic a guide to completeness theorems and their applications |
| title_auth | The mathematics of logic a guide to completeness theorems and their applications |
| title_exact_search | The mathematics of logic a guide to completeness theorems and their applications |
| title_exact_search_txtP | The mathematics of logic a guide to completeness theorems and their applications |
| title_full | The mathematics of logic a guide to completeness theorems and their applications Richard Kaye |
| title_fullStr | The mathematics of logic a guide to completeness theorems and their applications Richard Kaye |
| title_full_unstemmed | The mathematics of logic a guide to completeness theorems and their applications Richard Kaye |
| title_short | The mathematics of logic |
| title_sort | the mathematics of logic a guide to completeness theorems and their applications |
| title_sub | a guide to completeness theorems and their applications |
| topic | Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Mathematische Logik |
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