A first journey through logic:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2019]
|
| Schriftenreihe: | Student Mathematical Library
volume 89 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031489386&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xi, 185 Seiten |
| ISBN: | 9781470452728 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Introduction Chapter 1. ix Counting to Infinity 1 Introduction 1 §1.1. Naive Set Theory 1 §1.2. The Cantor and Cantor-Bernstein Theorems 2 §1.3. Orders 3 §1.4. Operations on Orders 5 §1.5. Ordinal Numbers 7 §1.6. Ordinal Arithmetic 11 §1.7. The Axiom of Choice 14 §1.8. Cardinal Numbers 14 §1.9. Operations on Cardinals 16 §1.10. Cofinality 19 §1.11. Exercises 22 §1.12. Appendix: Hindman’s Theorem 28 Chapter 2. First-order Logic Introduction 33 33 v
VI Contents §2.1. Languages and Structures 34 §2.2. Terms and Formulas 36 §2.3. Semantics 39 §2.4. Substitution 41 §2.5. Universally Valid Formulas 45 §2.6. Formal Proofs and Gôdeľs Completeness Theorem 48 §2.7. Exercises 58 Chapter 3. First Steps in Model Theory 65 Introduction 65 §3.1. Some Fundamental Theorems 66 §3.2. The Diagram Method 70 §3.3. Expansions by Definition 72 §3.4. Quantifier Elimination 75 §3.5. Algebraically Closed Fields 78 §3.6. Ax’s Theorem 81 §3.7. Exercises 83 Chapter 4. Recursive Functions 89 Introduction 89 §4.1. Primitive Recursive Functions 90 §4.2. The Ackermann Function 94 §4.3. Partial Recursive Functions 96 §4.4. Turing Computable Functions 98 §4.5. Universal Functions 107 §4.6. Recursively Enumerable Sets 109 §4.7. Elimination of Recursion 113 §4.8. Exercises 115 Chapter 5. Models of Arithmetic and Limitation Theorems 119 Introduction 119 §5.1. 120 Coding Formulas and Proofs
Contents vii §5.2. Decidable Theories 122 §5.3. Peano Arithmetic 125 §5.4. The Theorems of Tarski and Church 131 §5.5. Gôdeľs First Incompleteness Theorem 133 §5.6. Definability of Satisfiability for Eļ-formulas 134 §5.7. Gôdeľs Second Incompleteness Theorem 137 §5.8. Exercises 141 Chapter 6. Axiomatic Set Theory 147 Introduction 147 §6.1. The Framework 147 §6.2. The Zermelo-Fraenkel Axioms 148 §6.3. The Axiom of Choice 155 §6.4. The von Neumann Hierarchy and the Axiom of Foundation 157 Some Results on Incompleteness, Independence and Relative Consistency 161 A Glimpse of Further Independence andRelative Consistency Results 169 Exercises 173 §6.5. §6.6. §6.7. Bibliography 179 Index 181
|
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| id | DE-604.BV046108732 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T18:43:23Z |
| institution | BVB |
| isbn | 9781470452728 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031489386 |
| oclc_num | 1129406615 |
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| physical | xi, 185 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Student Mathematical Library |
| series2 | Student Mathematical Library |
| spellingShingle | Hils, Martin 1973- Loeser, François A first journey through logic Student Mathematical Library Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | A first journey through logic |
| title_auth | A first journey through logic |
| title_exact_search | A first journey through logic |
| title_full | A first journey through logic Martin Hils, François Loeser |
| title_fullStr | A first journey through logic Martin Hils, François Loeser |
| title_full_unstemmed | A first journey through logic Martin Hils, François Loeser |
| title_short | A first journey through logic |
| title_sort | a first journey through logic |
| topic | Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Mathematische Logik |
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