Introduction to mathematical logic:
"Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. Th...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2010
|
| Edition: | 5. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Godel, Church, Kleene, Rosser, and Turing."--BOOK JACKET. |
| Physical Description: | XXIV, 469 S. |
| ISBN: | 1584888768 9781584888765 |
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| 520 | 1 | |a "Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Godel, Church, Kleene, Rosser, and Turing."--BOOK JACKET. | |
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Record in the Search Index
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| adam_text | Titel: Introduction to mathematical logic
Autor: Mendelson, Elliott
Jahr: 2010
Contents
Preface.................................................................................................................. xiii
Introduction..........................................................................................................xv
1. The Propositional Calculus............................................................................1
1.1 Propositional Connectives. Truth Tables..........................................1
1.2 Tautologies............................................................................................5
1.3 Adequate Sets of Connectives..........................................................18
1.4 An Axiom System for the Propositional Calculus........................24
1.5 Independence. Many-Valued Logics...............................................34
1.6 Other Axiomatizations......................................................................37
2. First-Order Logic and Model Theory.........................................................41
2.1 Quantifiers...........................................................................................41
2.1.1 Parentheses............................................................................44
2.2 First-Order Languages and Their Interpretations.
Satisfiability and Truth. Models....................................................48
2.3 First-Order Theories...........................................................................61
2.3.1 Logicai Axioms......................................................................62
2.3.2 Proper Axioms......................................................................62
2.3.3 Rules of Inference.................................................................62
2.4 Properties of First-Order Theories...................................................64
2.5 Additional Metatheorems and Derived Rules...............................69
2.5.1 Particularization Rule A4....................................................69
2.5.2 Existential Rule E4................................................................69
2.6 Rule C..................................................................................................73
2.7 Completeness Theorems...................................................................77
2.8 First-Order Theories with Equality..................................................88
2.9 Definitions of New Function Lettere
and Individuai Constants.................................................................97
2.10 Prenex Normal Forms.....................................................................100
2.11 Isomorphism of Interpretations. Categoricity of Theories.........105
2.12 Generalized First-Order Theories. Completeness
and Decidability...............................................................................107
2.12.1 Mathematical Applications..............................................Ili
2.13 Elementary Equivalence. Elementaiy Extensions........................117
2.14 Ultrapowers. Nonstandard Analysis..........................................123
2.14.1 Reduced Direct Products.................................................125
2.14.2 Nonstandard Analysis.....................................................131
2.15 Semantic Trees..................................................................................135
2.16 Quantification Theory AUowing Empty Domains......................141
Contents
3. Formai Number Theory..............................................................................149
3.1 An Axiom System..............................................................................149
3.2 Number-Theoretic Functions and Relations..................................166
3.3 Primitive Recursive and Recursive Functions...............................171
3.4 Arithmetization. Godei Numbers....................................................188
3.5 The Fixed-Point Theorem. Gòdel s
Incompleteness Theorem...................................................................202
3.6 Recursive Undecidability. Church s Theorem...............................214
3.7 Nonstandard Models.........................................................................224
4. Axiomatic Set Theory..................................................................................227
4.1 An Axiom System..............................................................................227
4.2 Ordinai Numbers...............................................................................242
4.3 Equinumerosity. Finite and Denumerable Sets.............................256
4.3.1 Finite Sets...............................................................................261
4.4 Hartogs Theorem. Initial Ordinals. Ordinai Arithmetic............266
4.5 The Axiom of Choice. The Axiom of Regularity...........................279
4.6 Other Axiomatizations of Set Theory..............................................290
4.6.1 Morse-Kelley (MK)..............................................................291
4.6.2 Zermelo-Fraenkel (ZF)........................................................291
4.6.3 The Theory of Types (ST)....................................................293
4.6.3.1 STI (Extensionality Axiom)..................................294
4.6.3.2 ST2 (Comprehension
Axiom Scheme)......................................................294
4.6.3.3 ST3 (Axiom of Infinity).........................................295
4.6.4 Quine s Theories NF and ML.............................................297
4.6.4.1 NF1 (Extensionality)..............................................297
4.6.4.2 NF2 (Comprehension)...........................................298
4.6.5 Set Theory with Urelements...............................................300
5. Computability...............................................................................................309
5.1 Algorithms. Turing Machines..........................................................309
5.2 Diagrams.............................................................................................315
5.3 Partial Recursive Functions. Unsolvable Problems.......................322
5.4 The Kleene-Mostowski Hierarchy. Recursively
Enumerable Sets.................................................................................338
5.5 Other Notions of Computability......................................................350
5.6 Decision Problems..............................................................................368
Appendix A: Second-Order Logic..................................................................375
Appendix B: First Steps in Modal Propositional Logic.............................391
Contents xi
Answers to Selected Exercises........................................................................403
Bibliography.......................................................................................................433
Notation...............................................................................................................447
Index....................................................................................................................453
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| discipline | Mathematik Philosophie |
| edition | 5. ed. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:43:43Z |
| institution | BVB |
| isbn | 1584888768 9781584888765 |
| language | English |
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| physical | XXIV, 469 S. |
| publishDate | 2010 |
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| publisher | CRC Press |
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| spelling | Mendelson, Elliott 1931- Verfasser (DE-588)121929035 aut Introduction to mathematical logic Elliott Mendelson 5. ed. Boca Raton [u.a.] CRC Press 2010 XXIV, 469 S. txt rdacontent n rdamedia nc rdacarrier "Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Godel, Church, Kleene, Rosser, and Turing."--BOOK JACKET. Logic, Symbolic and mathematical Logic, Symbolic and mathematical Problems, exercises, etc. Mathematische Logik (DE-588)4037951-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung 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=017753949&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mendelson, Elliott 1931- Introduction to mathematical logic Logic, Symbolic and mathematical Logic, Symbolic and mathematical Problems, exercises, etc. Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4151278-9 |
| title | Introduction to mathematical logic |
| title_auth | Introduction to mathematical logic |
| title_exact_search | Introduction to mathematical logic |
| title_full | Introduction to mathematical logic Elliott Mendelson |
| title_fullStr | Introduction to mathematical logic Elliott Mendelson |
| title_full_unstemmed | Introduction to mathematical logic Elliott Mendelson |
| title_short | Introduction to mathematical logic |
| title_sort | introduction to mathematical logic |
| topic | Logic, Symbolic and mathematical Logic, Symbolic and mathematical Problems, exercises, etc. Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Logic, Symbolic and mathematical Problems, exercises, etc. Mathematische Logik Einführung |
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