Lectures on mathematical logic: 3 The logic of arithmetic
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Gordon & Breach
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 300 S. |
| ISBN: | 9056992686 |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Introduction 1
1. The Problem of Consistency 1
2. Completeness and Decidability 3
3. The Historical Setting 5
1. Consistency, Decidability, Completeness for the Arithmetic of
Order with Successor 10
1. Examples of simple Consistency Proofs 10
2. The Arithmetic Cj of Order with Successor 14
3. Reductions and Quantifier Elimination for Ci 16
4. The Main Theorems of the Arithmetic Cx 31
2. Consistency, Decidability, Completeness for the Arithmetic of
Addition and Order 34
1. The Arithmetic C2 of Addition and Order 34
2. Reductions and Quantifier Elimination for C2* 41
3. The Main Theorems for the Arithmetic C2* and C2 50
4. C2 and Induction 53
Introduction to Chapters 3 9 56
3. Antinomies, Pseudomenos, and their Analysis 58
1. Antinomies 58
2. More Examples and the Liar 59
3. Analysis: The Undefinability of Truth 61
4. Analysis: Incompleteness 67
4. Undefinability and Incompleteness, General Theory 71
1. A Combinatorial Frame 71
2. Basic Notions on Definability and Representability 73
3. Undefinability 80
4. Incompleteness 84
5. Incompleteness, continued 90
6. Set Theory an Example 94
5. Elementary and Primitive Recursive Functions 99
1. Basic Constructions 100
2. Simple Functions 107
3. Elementary Functions Ill
4. Primitive Recursive Functions 117
5. Elementary Arithmetization 120
6. Simple Arithmetization 125
v
vi Contents
6. Recursive Relations and Recursive Functions 132
1. Bounded Arithmetical Relations . . . ., 133
2. Projections 137
3. P closed Classes and their Core 140
4. Recursively Enumerable Relations 143
5. Recursive Relations and Recursive Functions 145
6. Recursivity and Minimization 148
7. The Arithmetization of Syntax 155
8. Consequences of Arithmetization 165
1. Recursively Enumerable Axiom Systems 166
2. Undefinability and Incompleteness 169
3. Radical Undecidability 174
4. Uniformization 178
9. Axioms for Arithmetic 190
1. The Arithmetic PC 191
2. The Arithmetic PB 196
3. Representability of Recursive Relations I 202
4. Representability of Recursive Relations II 205
5. Formal Definability of Recursive Relations 210
6. The Arithmetic PQ 212
7. Application: The Undecidability of Elementary Logic 216
10. Peano Arithmetic PA and its Expansion PR 219
1. Development of Basic Arithmetic 222
2. Extensions by Recursive Terms 231
3. A First Look at PR 240
11. Unprovability of Consistency 255
1. Introduction: Godel s Theorem and Provability Conditions . 255
Plan of the Remaining Sections of this Chapter 259
2. Free Variable Formalization of Syntax 262
PR Terms for Terms 262
PR Terms for Formulas 263
PR Terms for Deductions and the Proof Predicate 266
3. Interealization 271
The Internal Copy 271
Internalization and Codification 274
Internalization of Constants 277
Internal Forms 278
4. Sentences Which Imply Their Provability 283
Epilogue 292
Index of concepts and names 296
Index of symbolic notations 299
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| spelling | Felscher, Walter Verfasser aut Lectures on mathematical logic 3 The logic of arithmetic Walter Felscher Amsterdam Gordon & Breach 2000 X, 300 S. txt rdacontent n rdamedia nc rdacarrier Mathematische Logik (DE-588)4037951-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 (DE-604)BV012947413 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008816354&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Lectures on mathematical logic |
| title_auth | Lectures on mathematical logic |
| title_exact_search | Lectures on mathematical logic |
| title_full | Lectures on mathematical logic 3 The logic of arithmetic Walter Felscher |
| title_fullStr | Lectures on mathematical logic 3 The logic of arithmetic Walter Felscher |
| title_full_unstemmed | Lectures on mathematical logic 3 The logic of arithmetic Walter Felscher |
| title_short | Lectures on mathematical logic |
| title_sort | lectures on mathematical logic the logic of arithmetic |
| topic | Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Mathematische Logik Einführung |
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