Mathematical logic: a course with exercises 2 Recursion theory, Gödel's theorems, set theory, model theory
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2001
|
| Edition: | 1. publ. in English |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 331 S. graph. Darst. |
| ISBN: | 0198500513 0198500505 |
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| adam_text | MATHEMATICAL LOGIC A COURSE WITH EXERCISES PART II: RECURSION THEORY,
GODEL S THEOREMS, SET THEORY, MODEL THEORY RENE CORI AND DANIEL LASCAR
EQUIPE DE LOGIQUE MATHIMATIQUE UNIVERSITY PARIS VII TRANSLATED BY DONALD
H. PELLETIER YORK UNIVERSITY, TORONTO OXFORD UNIVBKMTY PKS8S CONTENTS
CONTENTS OF PART I XIV NOTES FROM THE TRANSLATOR XVII NOTES TO THE
READER XVIII INTRODUCTION 1 5 RECURSION THEORY 7 5.1 PRIMITIVE RECURSIVE
FUNCTIONS AND SETS 8 5.1.1 SOME INITIAL DEFINITIONS 8 5.1.2 EXAMPLES AND
CLOSURE PROPERTIES 10 5.1.3 CODING OF SEQUENCES 15 5.2 RECURSIVE
FUNCTIONS 18 5.2.1 ACKERMAN S FUNCTION 18 5.2.2 THE ^-OPERATOR AND THE
PARTIAL RECURSIVE FUNCTIONS 22 5.3 TURING MACHINES 25 5.3.1 DESCRIPTION
OF TURING MACHINES 25 5.3.2 R-COMPUTABLE FUNCTIONS 27 5.3.3 R-COMPUTABLE
PARTIAL FUNCTIONS ARE RECURSIVE 32 5.3.4 UNIVERSAL TURING MACHINES 36
5.4 RECURSIVELY ENUMERABLE SETS 40 5.4.1 RECURSIVE AND RECURSIVELY
ENUMERABLE SETS 40 5.4.2 THE HALTING PROBLEM 44 5.4.3 THE SMN THEORE M
46 5.4.4 THE FIXED POINT THEOREMS 50 5.5 EXERCISES FOR CHAPTER 5 54 6
FORMALIZATION OF ARITHMETIC, GODEL S THEOREMS 63 6.1 PEANO S AXIOMS 64
6.1.1 THE AXIOMS 64 6.1.2 THE ORDERING ON THE INTEGERS 69 6.2
REPRESENTABLE FUNCTIONS 73 6.3 ARITHMETIZATION OF SYNTAX 78 6.3.1 THE
CODING OF FORMULAS 78 6.3.2 THE CODING OF PROOFS 83 XU CONTENTS 6.4
INCOMPLETENESS AND UNDECIDABILITY THEOREMS 88 6.4.1 UNDECIDABILITY OF
ARITHMETIC AND PREDICATE CALCULUS 88 6.4.2 GODEL S INCOMPLETENESS
THEOREMS 90 6.5 EXERCISES FOR CHAPTER 6 100 7 SET THEORY 108 7.1 THE
THEORIES Z AND ZF 109 7.1.1 THE AXIOMS 109 7.1.2 ORDERED PAIRS,
RELATIONS, AND MAPS 116 7.2 ORDINAL NUMBERS AND INTEGERS 120 7.2.1
WELL-ORDERED SETS 120 7.2.2 THE ORDINALS 122 7.2.3 OPERATIONS ON ORDINAL
NUMBERS 129 7.2.4 THE INTEGERS 133 7.3 INDUCTIVE PROOFS AND DEFINITIONS
134 7.3.1 INDUCTION 134 7.3.2 THE AXIOM OF CHOICE 138 7.4 CARDINALITY
140 7.4.1 CARDINAL EQUIVALENCE CLASSES 140 7.4.2 OPERATIONS ON CARDINAL
EQUIVALENCE CLASSES 143 7.4.3 THE FINITE CARDINALS 146 7.4.4 COUNTABLE
SETS 148 7.4.5 THE CARDINAL NUMBERS 151 7.5 THE AXIOM OF FOUNDATION AND
THE REFLECTION SCHEMES 157 7.5.1 THE AXIOM OF FOUNDATION 157 7.5.2 SOME
RELATIVE CONSISTENCY RESULTS 160 7.5.3 INACCESSIBLE CARDINALS 164 7.5.4
THE REFLECTION SCHEME 166 7.6 EXERCISES FOR CHAPTER 7 171 8 SOME MODEL
THEORY 179 8.1 ELEMENTARY SUBSTRUCTURES AND EXTENSIONS 180 8.1.1
ELEMENTARY SUBSTRUCTURES 180 8.1.2 THE TARSKI-VAUGHT TEST 183 8.2
CONSTRUCTION OF ELEMENTARY EXTENSIONS 186 8.2.1 ELEMENTARY MAPS 186
8.2.2 THE METHOD OF DIAGRAMS 187 8.3 THE INTERPOLATION AND DEFINABILITY
THEOREMS 193 8.4 REDUCED PRODUCTS AND ULTRAPRODUCTS 199 8.5 PRESERVATION
THEOREMS 205 8.5.1 PRESERVATION BY SUBSTRUCTURES 205 8.5.2 PRESERVATION
BY UNIONS OF CHAINS 208 8.5.3 PRESERVATION BY REDUCED PRODUCTS 211
CONTENTS XIIL 8.6 KO-CATEGORICAL THEORIES 217 8.6.1 THE OMITTING TYPES
THEOREM 217 8.6.2 KO-CATEGORICAL STRUCTURES 222 8.7 EXERCISES FOR
CHAPTER 8 229 SOLUTIONS TO THE EXERCISES OF PART II CHAPTER 5 240
CHAPTER 6 260 CHAPTER 7 277 CHAPTER 8 298 BIBLIOGRAPHY 325 INDEX 327
|
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| indexdate | 2024-07-09T18:56:17Z |
| institution | BVB |
| isbn | 0198500513 0198500505 |
| language | English |
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| physical | XX, 331 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Cori, René Verfasser aut Logique mathématique Mathematical logic a course with exercises 2 Recursion theory, Gödel's theorems, set theory, model theory René Cori and Daniel Lascar 1. publ. in English Oxford [u.a.] Oxford Univ. Press 2001 XX, 331 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lascar, Daniel Verfasser aut (DE-604)BV013052001 2 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009601389&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cori, René Lascar, Daniel Mathematical logic a course with exercises |
| title | Mathematical logic a course with exercises |
| title_alt | Logique mathématique |
| title_auth | Mathematical logic a course with exercises |
| title_exact_search | Mathematical logic a course with exercises |
| title_full | Mathematical logic a course with exercises 2 Recursion theory, Gödel's theorems, set theory, model theory René Cori and Daniel Lascar |
| title_fullStr | Mathematical logic a course with exercises 2 Recursion theory, Gödel's theorems, set theory, model theory René Cori and Daniel Lascar |
| title_full_unstemmed | Mathematical logic a course with exercises 2 Recursion theory, Gödel's theorems, set theory, model theory René Cori and Daniel Lascar |
| title_short | Mathematical logic |
| title_sort | mathematical logic a course with exercises recursion theory godel s theorems set theory model theory |
| title_sub | a course with exercises |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009601389&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013052001 |
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