Elements of mathematical logic: (model theory)
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
North-Holland
1971
|
| Edition: | 2., rev. print. |
| Series: | Studies in logic and the foundations of mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 231 S. |
| ISBN: | 0720422655 |
Staff View
MARC
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| 245 | 1 | 0 | |a Elements of mathematical logic |b (model theory) |c G. Kreisel ; J. L. Krivine |
| 250 | |a 2., rev. print. | ||
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Record in the Search Index
| _version_ | 1804119894560604160 |
|---|---|
| adam_text | CONTENTS
page
0. Preliminaries : Definition schemas 1
1. Propositional calculus 4
Exercises 8
2. Predicate calculus 15
Exercises 29
3. Predicate calculus with equality 34
Exercises 41
4. Elimination of quantifiers 49
Dense orders with first and last element 51
Discrete orders without first or last element 53
Some commutative groups with discrete total orderings ... 54
Algebraically closed fields 57
Real closed fields 60
Seperable Boolean rings 65
Exercises 71
5. Predicate calculus with several types of objects: the
hierarchy of finite types 80
Predicate calculus with equality, with k types of objects, without
function symbols 89
Predicate calculus with equality, with k types of objects, including
function symbols 93
Finite type structure 95
Hierarchy of finite types ... 96
Principal models 98
Exercises 101
xvi contents
6. Definability 115
Invariance and stability 116
Invariance and stability: hierarchy of finite types 118
Rigidity 120
Definability in C realizations 122
Exercises 125
7. Principal models: models of infinite formulas .... 136
Principal models: formulas of finite order 137
Principal models: some formulas of second order .... 140
Infinite formulas which define finitary relations 142
Countable languages: countable sets of infinite formulas . . 144
Exercises 145
Appendix i. The axiomatic method 154
Appendix ii. Foundations of mathematics 160
Part A. Set theoretic semantic foundations 170
1. Analysis of intuitive mathematics in set theoretic terms 171
Intuitive notion of ordinal 174
2. Formulation of laws for the basic set theoretic notions 175
Zermelo s axioms 180
Simple incompleteness results 181
Godel s incompleteness theorem 183
3. New axioms for the set theoretic notions: axioms of
infinity 192
4. Analysis of the intuitive notion of logical validity . . 195
First order languages: Godel s completeness theorem . 195
Second order languages 196
A privileged position for finite first order formulas and
first order consequence? 197
Part B. Combinatorial foundations 203
0. Combinatorial reasoning 205
Translation into set theoretic terms 212
CONTENTS XVII
1. Analysis of intuitive mathematics in combinatorial terms 214
Hilbert s consistency problem 215
Positive results on Hilbert s problem 217
2. Formulation of laws for the basic combinatorial notions 220
Incompleteness results 222
Consequences for Hilbert s problem 223
3. Developments of the theory 224
4. Critical discussion 226
Defects of doctrinaire foundations 227
Defects of crude formalism 228
Open problems 229
5. Current directions of research 229
Part C. Semantic versus syntactic (combinatorial) introduction
mathematical logic 232
|
| any_adam_object | 1 |
| author | Kreisel, Georg 1923-2015 Krivine, Jean-Louis |
| author_GND | (DE-588)119528592 |
| author_facet | Kreisel, Georg 1923-2015 Krivine, Jean-Louis |
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| author_sort | Kreisel, Georg 1923-2015 |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 510.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.1 |
| dewey-search | 510.1 |
| dewey-sort | 3510.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 2., rev. print. |
| format | Book |
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| indexdate | 2024-07-09T16:33:27Z |
| institution | BVB |
| isbn | 0720422655 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003565793 |
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| physical | XVII, 231 S. |
| psigel | HUB-ZB011201002 |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | North-Holland |
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| series2 | Studies in logic and the foundations of mathematics |
| spelling | Kreisel, Georg 1923-2015 Verfasser (DE-588)119528592 aut Elements of mathematical logic (model theory) G. Kreisel ; J. L. Krivine 2., rev. print. Amsterdam North-Holland 1971 XVII, 231 S. txt rdacontent n rdamedia nc rdacarrier Studies in logic and the foundations of mathematics Logique symbolique et mathématique Modèles mathématiques Modèles, Théorie des Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Grundlage (DE-588)4158388-7 s 1\p DE-604 Modelltheorie (DE-588)4114617-7 s 2\p DE-604 Krivine, Jean-Louis Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565793&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kreisel, Georg 1923-2015 Krivine, Jean-Louis Elements of mathematical logic (model theory) Logique symbolique et mathématique Modèles mathématiques Modèles, Théorie des Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd Grundlage (DE-588)4158388-7 gnd Modelltheorie (DE-588)4114617-7 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4158388-7 (DE-588)4114617-7 |
| title | Elements of mathematical logic (model theory) |
| title_auth | Elements of mathematical logic (model theory) |
| title_exact_search | Elements of mathematical logic (model theory) |
| title_full | Elements of mathematical logic (model theory) G. Kreisel ; J. L. Krivine |
| title_fullStr | Elements of mathematical logic (model theory) G. Kreisel ; J. L. Krivine |
| title_full_unstemmed | Elements of mathematical logic (model theory) G. Kreisel ; J. L. Krivine |
| title_short | Elements of mathematical logic |
| title_sort | elements of mathematical logic model theory |
| title_sub | (model theory) |
| topic | Logique symbolique et mathématique Modèles mathématiques Modèles, Théorie des Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd Grundlage (DE-588)4158388-7 gnd Modelltheorie (DE-588)4114617-7 gnd |
| topic_facet | Logique symbolique et mathématique Modèles mathématiques Modèles, Théorie des Logic, Symbolic and mathematical Mathematische Logik Grundlage Modelltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003565793&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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