Models and ultraproducts: an introd.
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Amsterdam
North-Holland Publ. [u.a.]
1974
|
| Edition: | 3., rev. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 322 S. |
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| 245 | 1 | 0 | |a Models and ultraproducts |b an introd. |
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Record in the Search Index
| _version_ | 1804135840551534592 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION 1
Ch. 0 PREREQUISITES 4
Ch. 1 BOOLEAN ALGEBRAS 7
1. Lattices 7 2. Filters 12 3. Ultrafilters 14
4. Homomorphisms and quotient algebras 17 5. Filters in
topology 22 6. The Stone representation theorem 23
7. Atomless Boolean algebras and, Cantor spaces 27
8. Historical and bibliographical remarks 31
Ch. 2 PROPOSITIONAL CALCULUS 32
1. The system SC 32 2. The Lindenbaum algebra 40
3. The completeness of propositional calculus 42 4. The
compactness of propositional calculus 44 5. Historical and
bibliographical remarks 49
Ch. 3 PREDICATE CALCULUS 50
1. The language L 50 2. Interpretations of L 54
3. An axiom system for predicate calculus 57 4. The Linden¬
baum algebra ot PC 61 5. The completeness of PC 62
6. Uncountable languages 67 7. Constants 68
8. Function symbols 69 9. Historical and bibliographical
remarks 71
Ch. 4 BEGINNING MODEL THEORY 72
1. The basic notions 72 2. Unions of chains 79
3. Lowenheim Skolem theorems 80 4. Hanf numbers 84
5. Historical and bibliographical remarks 86
VIII CONTENTS
Ch. 5 INTRODUCING ULTRAPRODUCTS 87
1. The ultraproduct construction 87 2. LoS s theorem 89
3. Finite axiomatizability 92 4. The compactness theorem 102/
5. The completeness theorem, the axiom of choice and the ultrafilter
theorem 103 6. Historical and bibliographical remarks 106
Ch. 6 SET THEORETIC PROPERTIES OF ULTRAPRODUCTS 107
1. More about ultrafilters 107 2. Set theoretic properties of
ultraproducts 122 3. The cardinality of ultraproducts 125
4. Well ordered ultraproducts 133 5. The Rabin Keisler
theorem 136 6. Historical and bibliographical remarks 139
Ch. 7 ELEMENTARY CLASSES 140
1. The various sorts of elementary classes 140 2. Keisler s
ultrapower theorem 145 3. Characterizing elementary
classes 151 4. Craig s interpolation lemma 153
5. EC as a Boolean algebra 157 6. Historical and biblio¬
graphical remarks 159
Ch. 8 ULTRALIMITS 161
1. Two basic lemmas 161 2. Ultralimits 165
3. Elementary classes and ultralimits 169 4. Ultralimits and
Craig s interpolation lemma 170 5. Historical and biblio¬
graphical remarks 174
Ch. 9 COMPLETENESS AND MODEL COMPLETENESS 175
1. Completeness 175 2. Model completeness 183
3. Universal and existential sentences 185 4. A test for model
completeness 188 5. Applications of Robinson s test 191
6. Historical and bibliographical remarks 200
Ch. 10 HOMOGENEOUS AND UNIVERSAL STRUCTURES 201
1. The main definitions 201 2. The uniqueness of Jl homo¬
geneous, uf universal structures 204 3. The existence of 41
homogeneous, uf universal structures 4. Full expansions
213 5. Historical and bibliographical remarks 216
CONTENTS IX
Ch. 11 SATURATED MODELS 217
1. Saturated models 217 2. Ultraproducts and saturated
structures 222 3. More about saturated structures 224
4. Special relational structures 229 s Historical and biblio¬
graphical remarks 232
Ch. 12 APPLICATIONS OF ULTRAPRODUCTS 233
1. Godel s completeness proof 233 2. A non standard
model of arithmetic 236 3. MacDowell and Specker s
theorem 240 4. Cardinal like orderings 244 5. Two
cardinal theorems 245 6. Vaught s two cardinal theorem
249 7. Chang s two cardinal theorem 253 8. Historical
and bibliographical remarks 259
Ch. 13 GENERALIZED QUANTIFIERS 260
1. Generalized quantifiers 261 2. The quantifiers Q* 262
3. The Chang quantifier 267 4. Fuhrken s reduction tech¬
nique 270 5. Lowenheim Skolem and compactness theorems
for Lq 275 6. Completeness theorem for LQ 279
7. Historical and bibliographical remarks 285
Ch. 14 INFINITARY LANGUAGES 286
1. The language La/3 286 2. The compactness property;
incompactness results for accessible cardinals 289 3. In
compactness results for inaccessible cardinals 293 4. Meas¬
urable cardinals 295 5. Keisler s ultrapower proof 298
6. Measurable cardinals and the axiom of constructibility 300
7. Historical and bibliographical remarks 305
SOME SUGGESTIONS FOR FURTHER READING 308
BIBLIOGRAPHY 309
INDEX OF NAMED THEOREMS 317
GENERAL INDEX 319
|
| adam_txt |
CONTENTS
INTRODUCTION 1
Ch. 0 PREREQUISITES 4
Ch. 1 BOOLEAN ALGEBRAS 7
1. Lattices 7 2. Filters 12 3. Ultrafilters 14
4. Homomorphisms and quotient algebras 17 5. Filters in
topology 22 6. The Stone representation theorem 23
7. Atomless Boolean algebras and, Cantor spaces 27
8. Historical and bibliographical remarks 31
Ch. 2 PROPOSITIONAL CALCULUS 32
1. The system SC 32 2. The Lindenbaum algebra 40
3. The completeness of propositional calculus 42 4. The
compactness of propositional calculus 44 5. Historical and
bibliographical remarks 49
Ch. 3 PREDICATE CALCULUS 50
1. The language L 50 2. Interpretations of L 54
3. An axiom system for predicate calculus 57 4. The Linden¬
baum algebra ot PC 61 5. The completeness of PC 62
6. Uncountable languages 67 7. Constants 68
8. Function symbols 69 9. Historical and bibliographical
remarks 71
Ch. 4 BEGINNING MODEL THEORY 72
1. The basic notions 72 2. Unions of chains 79
3. Lowenheim Skolem theorems 80 4. Hanf numbers 84
5. Historical and bibliographical remarks 86
VIII CONTENTS
Ch. 5 INTRODUCING ULTRAPRODUCTS 87
1. The ultraproduct construction 87 2. LoS's theorem 89
3. Finite axiomatizability 92 4. The compactness theorem 102/
5. The completeness theorem, the axiom of choice and the ultrafilter
theorem 103 6. Historical and bibliographical remarks 106
Ch. 6 SET THEORETIC PROPERTIES OF ULTRAPRODUCTS 107
1. More about ultrafilters 107 2. Set theoretic properties of
ultraproducts 122 3. The cardinality of ultraproducts 125
4. Well ordered ultraproducts 133 5. The Rabin Keisler
theorem 136 6. Historical and bibliographical remarks 139
Ch. 7 ELEMENTARY CLASSES 140
1. The various sorts of elementary classes 140 2. Keisler's
ultrapower theorem 145 3. Characterizing elementary
classes 151 4. Craig's interpolation lemma 153
5. EC as a Boolean algebra 157 6. Historical and biblio¬
graphical remarks 159
Ch. 8 ULTRALIMITS 161
1. Two basic lemmas 161 2. Ultralimits 165
3. Elementary classes and ultralimits 169 4. Ultralimits and
Craig's interpolation lemma 170 5. Historical and biblio¬
graphical remarks 174
Ch. 9 COMPLETENESS AND MODEL COMPLETENESS 175
1. Completeness 175 2. Model completeness 183
3. Universal and existential sentences 185 4. A test for model
completeness 188 5. Applications of Robinson's test 191
6. Historical and bibliographical remarks 200
Ch. 10 HOMOGENEOUS AND UNIVERSAL STRUCTURES 201
1. The main definitions 201 2. The uniqueness of Jl homo¬
geneous, uf universal structures 204 3. The existence of 41
homogeneous, uf universal structures 4. Full expansions
213 5. Historical and bibliographical remarks 216
CONTENTS IX
Ch. 11 SATURATED MODELS 217
1. Saturated models 217 2. Ultraproducts and saturated
structures 222 3. More about saturated structures 224
4. Special relational structures 229 s Historical and biblio¬
graphical remarks 232
Ch. 12 APPLICATIONS OF ULTRAPRODUCTS 233
1. Godel's completeness proof 233 2. A non standard
model of arithmetic 236 3. MacDowell and Specker's
theorem 240 4. Cardinal like orderings 244 5. Two
cardinal theorems 245 6. Vaught's two cardinal theorem
249 7. Chang's two cardinal theorem 253 8. Historical
and bibliographical remarks 259
Ch. 13 GENERALIZED QUANTIFIERS 260
1. Generalized quantifiers 261 2. The quantifiers Q* 262
3. The Chang quantifier 267 4. Fuhrken's reduction tech¬
nique 270 5. Lowenheim Skolem and compactness theorems
for Lq 275 6. Completeness theorem for LQ 279
7. Historical and bibliographical remarks 285
Ch. 14 INFINITARY LANGUAGES 286
1. The language La/3 286 2. The compactness property;
incompactness results for accessible cardinals 289 3. In
compactness results for inaccessible cardinals 293 4. Meas¬
urable cardinals 295 5. Keisler's ultrapower proof 298
6. Measurable cardinals and the axiom of constructibility 300
7. Historical and bibliographical remarks 305
SOME SUGGESTIONS FOR FURTHER READING 308
BIBLIOGRAPHY 309
INDEX OF NAMED THEOREMS 317
GENERAL INDEX 319 |
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| spelling | Bell, John L. 1945- Verfasser (DE-588)128411570 aut Models and ultraproducts an introd. 3., rev. print. Amsterdam North-Holland Publ. [u.a.] 1974 IX, 322 S. txt rdacontent n rdamedia nc rdacarrier Modelltheorie (DE-588)4114617-7 gnd rswk-swf Ultraprodukt (DE-588)4127046-0 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Modelltheorie (DE-588)4114617-7 s DE-604 Ultraprodukt (DE-588)4127046-0 s Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 Slomson, Alan B. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015111097&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 | Bell, John L. 1945- Slomson, Alan B. Models and ultraproducts an introd. Modelltheorie (DE-588)4114617-7 gnd Ultraprodukt (DE-588)4127046-0 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4127046-0 (DE-588)4037951-6 |
| title | Models and ultraproducts an introd. |
| title_auth | Models and ultraproducts an introd. |
| title_exact_search | Models and ultraproducts an introd. |
| title_exact_search_txtP | Models and ultraproducts an introd. |
| title_full | Models and ultraproducts an introd. |
| title_fullStr | Models and ultraproducts an introd. |
| title_full_unstemmed | Models and ultraproducts an introd. |
| title_short | Models and ultraproducts |
| title_sort | models and ultraproducts an introd |
| title_sub | an introd. |
| topic | Modelltheorie (DE-588)4114617-7 gnd Ultraprodukt (DE-588)4127046-0 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Modelltheorie Ultraprodukt Mathematische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015111097&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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