Mathematical logic: a course with exercises 1 Propositional calculus, Boolean algebras, predicate calculus
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2000
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| Edition: | 1. publ. in English |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 338 S. graph. Darst. |
| ISBN: | 0198500491 0198500483 |
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| adam_text | MATHEMATICAL LOGIC A COURSE WITH EXERCISES PART I: PROPOSITIONAL
CALCULUS, BOOLEAN ALGEBRAS, PREDICATE CALCULUS RENE CORI AND DANIEL
LASCAR EQUIPE DE LOGIQUE MATHIMATIQUE UNIVERSITY PARIS VII TRANSLATED BY
DONALD H. PELLETIER YORK UNIVERSITY, TORONTO OXFORD UNIVBR8ITY PKB8S
CONTENTS CONTENTS OF PART II NOTES FROM THE TRANSLATOR NOTES TO THE
READER INTRODUCTION 1 PREPOSITIONAL CALCULUS 1.1 1.2 1.3 1.4 1.5 1.6
SYNTAX 1.1.1 PREPOSITIONAL FORMULAS 1.1.2 PROOFS BY INDUCTION ON THE SET
OF FORMULAS 1.1.3 THE DECOMPOSITION TREE OF A FORMULA 1.1.4 THE UNIQUE
DECOMPOSITION THEOREM 1.1.5 DEFINITIONS BY INDUCTION ON THE SET OF
FORMULAS 1.1.6 SUBSTITUTIONS IN A PREPOSITIONAL FORMULA SEMANTICS 1.2.1
ASSIGNMENTS OF TRUTH VALUES AND TRUTH TABLES 1.2.2 TAUTOLOGIES AND
LOGICALLY EQUIVALENT FORMULAS 1.2.3 SOME TAUTOLOGIES NORMAL FORMS AND
COMPLETE SETS OF CONNECTIVES 1.3.1 OPERATIONS ON {0,1} AND FORMULAS
1.3.2 NORMAL FORMS 1.3.3 COMPLETE SETS OF CONNECTIVES THE INTERPOLATION
LEMMA 1.4.1 INTERPOLATION LEMMA 1.4.2 THE DEFINABILITY THEOREM THE
COMPACTNESS THEOREM 1.5.1 SATISFACTION OF A SET OF FORMULAS 1.5.2 THE
COMPACTNESS THEOREM FOR PROPOSITIONAL CALCULUS EXERCISES FOR CHAPTER 1 2
BOOLEAN ALGEBRAS 2.1 2.2 ALGEBRA AND TOPOLOGY REVIEW 2.1.1 ALGEBRA 2.1.2
TOPOLOGY 2.1.3 AN APPLICATION TO PROPOSITIONAL CALCULUS DEFINITION OF
BOOLEAN ALGEBRA 2.2.1 PROPERTIES OF BOOLEAN ALEEBRAS. ORDER RELATIONS
XIV XVI XVII 1 7 8 8 11 13 15 18 19 21 21 27 31 34 34 38 40 42 42 44 45
45 48 53 63 64 64 67 71 71 72 XII CONTENTS 2.3 2.4 2.5 2.6 2.7 2.2.2
BOOLEAN ALGEBRAS AS ORDERED SETS ATOMS IN A BOOLEAN ALGEBRA
HOMOMORPHISMS, ISOMORPHISMS, SUBALGEBRAS 2.4.1 HOMOMORPHISMS AND
ISOMORPHISMS 2.4.2 BOOLEAN SUBALGEBRAS IDEALS AND FILTERS 2.5.1
PROPERTIES OF IDEALS 2.5.2 MAXIMAL IDEALS 2.5.3 FILTERS 2.5.4
ULTRAFILTERS 2.5.5 FILTERBASES STONE S THEOREM 2.6.1 THE STONE SPACE OF
A BOOLEAN ALGEBRA 2.6.2 STONE S THEOREM 2.6.3 BOOLEAN SPACES ARE STONE
SPACES EXERCISES FOR CHAPTER 2 3 PREDICATE CALCULUS 3.1 3.2 3.3 3.4 3.5
3.6 SYNTAX 3.1.1 FIRST ORDER LANGUAGES 3.1.2 TERMS OF THE LANGUAGE 3.1.3
SUBSTITUTIONS IN TERMS 3.1.4 FORMULAS OF THE LANGUAGE 3.1.5 FREE
VARIABLES, BOUND VARIABLES, AND CLOSED FORMULAS 3.1.6 SUBSTITUTIONS IN
FORMULAS STRUCTURES 3.2.1 MODELS OF A LANGUAGE 3.2.2 SUBSTRUCTURES AND
RESTRICTIONS 3.2.3 HOMOMORPHISMS AND ISOMORPHISMS SATISFACTION OF
FORMULAS IN STRUCTURES 3.3.1 INTERPRETATION IN A STRUCTURE OF THE TERMS
3.3.2 SATISFACTION OF THE FORMULAS IN A STRUCTURE UNIVERSAL EQUIVALENCE
AND SEMANTIC CONSEQUENCE PRENEX FORMS AND SKOLEM FORMS 3.5.1 PRENEX
FORMS 3.5.2 SKOLEM FORMS FIRST STEPS IN MODEL THEORY 3.6.1 SATISFACTION
IN A SUBSTRUCTURE 3.6.2 ELEMENTARY EQUIVALENCE 3.6.3 THE LANGUAGE
ASSOCIATED WITH A STRUCTURE AND FORMULAS WITH PARAMETERS 3.6.4 FUNCTIONS
AND RELATIONS DEFINABLE IN A STRUCTURE 75 79 81 81 86 88 88 91 93 94 96
97 98 102 102 106 112 113 113 115 121 122 125 127 130 131 133 135 137
137 140 147 157 157 160 165 165 170 174 176 CONTENTS XLII 3.7 MODELS
THAT MAY NOT RESPECT EQUALITY 179 3.8 EXERCISES FOR CHAPTER 3 182 4 THE
COMPLETENESS THEOREMS 193 4.1 FORMAL PROOFS (OR DERIVATIONS) 194 4.1.1
AXIOMS AND RULES 194 4.1.2 FORMAL PROOFS 196 4.1.3 THE FINITENESS
THEOREM AND THE DEDUCTION THEOREM 200 4.2 HENKIN MODELS 202 4.2.1 HENKIN
WITNESSES 203 4.2.2 THE COMPLETENESS THEOREM 205 4.3 HERBRAND S METHOD
209 4.3.1 SOME EXAMPLES 209 4.3.2 THE AVATARS OF A FORMULA 212 4.4
PROOFS USING CUTS 217 4.4.1 THE CUT RULE 217 4.4.2 COMPLETENESS OF THE
METHOD 221 4.5 THE METHOD OF RESOLUTION 224 4.5.1 UNIFICATION 224 4.5.2
PROOFS BY RESOLUTION 230 4.6 EXERCISES FOR CHAPTER 4 241 SOLUTIONS TO
THE EXERCISES OF PART I CHAPTER 1 245 CHAPTER 2 270 CHAPTER 3 293
CHAPTER 4 320 BIBLIOGRAPHY 330 INDEX 332
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| discipline | Mathematik |
| edition | 1. publ. in English |
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| isbn | 0198500491 0198500483 |
| language | English |
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| spelling | Cori, René Verfasser aut Logique mathématique Mathematical logic a course with exercises 1 Propositional calculus, Boolean algebras, predicate calculus René Cori and Daniel Lascar 1. publ. in English Oxford [u.a.] Oxford Univ. Press 2000 XIX, 338 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cálculo proposicional larpcal Lógica matemática larpcal Logic, Symbolic and mathematical Lascar, Daniel Verfasser aut (DE-604)BV013052001 1 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009120065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cori, René Lascar, Daniel Mathematical logic a course with exercises Cálculo proposicional larpcal Lógica matemática larpcal Logic, Symbolic and mathematical |
| 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 1 Propositional calculus, Boolean algebras, predicate calculus René Cori and Daniel Lascar |
| title_fullStr | Mathematical logic a course with exercises 1 Propositional calculus, Boolean algebras, predicate calculus René Cori and Daniel Lascar |
| title_full_unstemmed | Mathematical logic a course with exercises 1 Propositional calculus, Boolean algebras, predicate calculus René Cori and Daniel Lascar |
| title_short | Mathematical logic |
| title_sort | mathematical logic a course with exercises propositional calculus boolean algebras predicate calculus |
| title_sub | a course with exercises |
| topic | Cálculo proposicional larpcal Lógica matemática larpcal Logic, Symbolic and mathematical |
| topic_facet | Cálculo proposicional Lógica matemática Logic, Symbolic and mathematical |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009120065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013052001 |
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