Model theory /:
This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians. Model theory is concerned with the notions of definition, interpre...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1993.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 42. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians. Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide variety of other areas such as set theory, geometry, algebra (in particular group theory), and computer science (e.g. logic programming and specification). Professor Hodges emphasises definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference. |
| Beschreibung: | 1 online resource (xiii, 772 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 716-754) and index. |
| ISBN: | 9781107087590 1107087597 0511551576 9780511551574 1139881671 9781139881678 1107102383 9781107102385 1107093848 9781107093843 |
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| 100 | 1 | |a Hodges, Wilfrid. | |
| 245 | 1 | 0 | |a Model theory / |c Wilfrid Hodges. |
| 264 | 1 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 1993. | |
| 300 | |a 1 online resource (xiii, 772 pages) : |b illustrations | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v volume 42 | |
| 504 | |a Includes bibliographical references (pages 716-754) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians. Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide variety of other areas such as set theory, geometry, algebra (in particular group theory), and computer science (e.g. logic programming and specification). Professor Hodges emphasises definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference. | ||
| 505 | 0 | |a Cover; Half-title; Encyclopedia of mathematics and its applications; Title; Copyright; Contents; Introduction; Note on notation; 1 Naming of parts; 1.1 Structures; 1.2 Homomorphisms and substructures; 1.3 Terms and atomic formulas; 1.4 Parameters and diagrams; 1.5 Canonical models; History And Bibliography; 2 Classifying structures; 2.1 Definable subsets; 2.2 Definable classes of structures; 2.3 Some notions from logic; 2.4 Maps and the formulas they preserve; 2.5 Classifying maps by formulas; 2.6 Translations; 2.7 Quantifier elimination; 2.8 Further examples; History and bibliography | |
| 505 | 8 | |a 3 Structures that look alike3.1 Theorems of skolem; 3.2 Back-and-forth equivalence; 3.3 Games for elementary equivalence; 3.4 Closed games; 3.5 Games and infinitary languages; 3.6 Clubs; History and bibliography; 4 Automorphisms; 4.1 Automorphisms; 4.2 Subgroups of small index; 4.3 Imaginary elements; 4.4 Eliminating imaginaries; 4.5 Minimal sets; 4.6 Geometries; 4.7 Almost strongly minimal theories; 4.8 Zil'ber's configuration; History and bibliography; 5 Interpretations; 5.1 Relativisation; 5.2 Pseudo-elementary Classes; 5.3 Interpreting one structure in another | |
| 505 | 8 | |a 5.4 Shapes and sizes of interpretations5.5 Theories that interpret anything; 5.6 Totally transcendental structures; 5.7 Interpreting groups and fields; History and bibliography; 6 The first-order case: compactness; 6.1 Compactness for first-order logic; 6.2 Boolean algebras and stone spaces; 6.3 Types; 6.4 Elementary amalgamation; 6.5 Amalgamation and preservation; 6.6 Expanding the language; 6.7 Stability; History and bibliography; 7 The countable case; 7.1 Fraisse's construction; 7.2 Omitting types; 7.3 Countable categoricity; 7.4 Cocategorical structures by fraisse's method | |
| 505 | 8 | |a History and bibliography8 The existential case; 8.1 Existentially closed structures; 8.2 Two methods of construction; 8.3 Model-completeness; 8.4 Quantifier elimination revisited; 8.5 More on e.c. models; 8.6 Amalgamation revisited; History and bibliography; 9 The Horn case: products; 9.1 Direct products; 9.2 Presentations; 9.3 Word-constructions; 9.4 Reduced products; 9.5 Ultraproducts; 9.6 The feferman-vaught theorem; 9.7 Boolean powers; History and bibliography; 10 Saturation; 10.1 The great and the good; 10.2 Big models exist; 10.3 Syntactic characterisations; 10.4 Special models | |
| 505 | 8 | |a 10.5 Definability10.6 Resplendence; 10.7 Atomic compactness; History and bibliography; 11 Combinatorics; 11.1 Indiscernibles; 11.2 Ehrenfeucht-Mostowski models; 11.3 Em models of unstable theories; 11.4 Nonstandard methods; 11.5 Defining well-orderings; 11.6 Infinitary indiscernibles; History and bibliography; 12 Expansions and categoricity; 12.1 One-cardinal and two-cardinal theorems; 12.2 Categoricity; 12.3 Cohomology of expansions; 12.4 Counting Expansions; 12.5 Relative categoricity; History and bibliography; Appendix: Examples; A.1 Modules; A.2 Abelian groups | |
| 546 | |a English. | ||
| 650 | 0 | |a Model theory. |0 http://id.loc.gov/authorities/subjects/sh85086421 | |
| 650 | 6 | |a Théorie des modèles. | |
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| 650 | 7 | |a Model theory |2 fast | |
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| 650 | 7 | |a Mathematische Logik |2 gnd |0 http://d-nb.info/gnd/4037951-6 | |
| 650 | 1 | 7 | |a Wiskundige modellen. |2 gtt |
| 650 | 7 | |a Lógica matemática. |2 larpcal | |
| 650 | 7 | |a Teoria dos modelos. |2 larpcal | |
| 650 | 7 | |a Modelos matemáticos. |2 larpcal | |
| 650 | 7 | |a Modèles, théorie des. |2 ram | |
| 776 | 0 | 8 | |i Print version: |a Hodges, Wilfrid. |t Model theory |z 0521304423 |w (DLC) 91025082 |w (OCoLC)24173886 |
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Datensatz im Suchindex
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| adam_text | |
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| author | Hodges, Wilfrid |
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| author_variant | w h wh |
| building | Verbundindex |
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| callnumber-first | Q - Science |
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| contents | Cover; Half-title; Encyclopedia of mathematics and its applications; Title; Copyright; Contents; Introduction; Note on notation; 1 Naming of parts; 1.1 Structures; 1.2 Homomorphisms and substructures; 1.3 Terms and atomic formulas; 1.4 Parameters and diagrams; 1.5 Canonical models; History And Bibliography; 2 Classifying structures; 2.1 Definable subsets; 2.2 Definable classes of structures; 2.3 Some notions from logic; 2.4 Maps and the formulas they preserve; 2.5 Classifying maps by formulas; 2.6 Translations; 2.7 Quantifier elimination; 2.8 Further examples; History and bibliography 3 Structures that look alike3.1 Theorems of skolem; 3.2 Back-and-forth equivalence; 3.3 Games for elementary equivalence; 3.4 Closed games; 3.5 Games and infinitary languages; 3.6 Clubs; History and bibliography; 4 Automorphisms; 4.1 Automorphisms; 4.2 Subgroups of small index; 4.3 Imaginary elements; 4.4 Eliminating imaginaries; 4.5 Minimal sets; 4.6 Geometries; 4.7 Almost strongly minimal theories; 4.8 Zil'ber's configuration; History and bibliography; 5 Interpretations; 5.1 Relativisation; 5.2 Pseudo-elementary Classes; 5.3 Interpreting one structure in another 5.4 Shapes and sizes of interpretations5.5 Theories that interpret anything; 5.6 Totally transcendental structures; 5.7 Interpreting groups and fields; History and bibliography; 6 The first-order case: compactness; 6.1 Compactness for first-order logic; 6.2 Boolean algebras and stone spaces; 6.3 Types; 6.4 Elementary amalgamation; 6.5 Amalgamation and preservation; 6.6 Expanding the language; 6.7 Stability; History and bibliography; 7 The countable case; 7.1 Fraisse's construction; 7.2 Omitting types; 7.3 Countable categoricity; 7.4 Cocategorical structures by fraisse's method History and bibliography8 The existential case; 8.1 Existentially closed structures; 8.2 Two methods of construction; 8.3 Model-completeness; 8.4 Quantifier elimination revisited; 8.5 More on e.c. models; 8.6 Amalgamation revisited; History and bibliography; 9 The Horn case: products; 9.1 Direct products; 9.2 Presentations; 9.3 Word-constructions; 9.4 Reduced products; 9.5 Ultraproducts; 9.6 The feferman-vaught theorem; 9.7 Boolean powers; History and bibliography; 10 Saturation; 10.1 The great and the good; 10.2 Big models exist; 10.3 Syntactic characterisations; 10.4 Special models 10.5 Definability10.6 Resplendence; 10.7 Atomic compactness; History and bibliography; 11 Combinatorics; 11.1 Indiscernibles; 11.2 Ehrenfeucht-Mostowski models; 11.3 Em models of unstable theories; 11.4 Nonstandard methods; 11.5 Defining well-orderings; 11.6 Infinitary indiscernibles; History and bibliography; 12 Expansions and categoricity; 12.1 One-cardinal and two-cardinal theorems; 12.2 Categoricity; 12.3 Cohomology of expansions; 12.4 Counting Expansions; 12.5 Relative categoricity; History and bibliography; Appendix: Examples; A.1 Modules; A.2 Abelian groups |
| ctrlnum | (OCoLC)861692081 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn861692081 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:39Z |
| institution | BVB |
| isbn | 9781107087590 1107087597 0511551576 9780511551574 1139881671 9781139881678 1107102383 9781107102385 1107093848 9781107093843 |
| language | English |
| oclc_num | 861692081 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xiii, 772 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Hodges, Wilfrid. Model theory / Wilfrid Hodges. Cambridge [England] ; New York : Cambridge University Press, 1993. 1 online resource (xiii, 772 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; volume 42 Includes bibliographical references (pages 716-754) and index. Print version record. This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians. Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide variety of other areas such as set theory, geometry, algebra (in particular group theory), and computer science (e.g. logic programming and specification). Professor Hodges emphasises definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference. Cover; Half-title; Encyclopedia of mathematics and its applications; Title; Copyright; Contents; Introduction; Note on notation; 1 Naming of parts; 1.1 Structures; 1.2 Homomorphisms and substructures; 1.3 Terms and atomic formulas; 1.4 Parameters and diagrams; 1.5 Canonical models; History And Bibliography; 2 Classifying structures; 2.1 Definable subsets; 2.2 Definable classes of structures; 2.3 Some notions from logic; 2.4 Maps and the formulas they preserve; 2.5 Classifying maps by formulas; 2.6 Translations; 2.7 Quantifier elimination; 2.8 Further examples; History and bibliography 3 Structures that look alike3.1 Theorems of skolem; 3.2 Back-and-forth equivalence; 3.3 Games for elementary equivalence; 3.4 Closed games; 3.5 Games and infinitary languages; 3.6 Clubs; History and bibliography; 4 Automorphisms; 4.1 Automorphisms; 4.2 Subgroups of small index; 4.3 Imaginary elements; 4.4 Eliminating imaginaries; 4.5 Minimal sets; 4.6 Geometries; 4.7 Almost strongly minimal theories; 4.8 Zil'ber's configuration; History and bibliography; 5 Interpretations; 5.1 Relativisation; 5.2 Pseudo-elementary Classes; 5.3 Interpreting one structure in another 5.4 Shapes and sizes of interpretations5.5 Theories that interpret anything; 5.6 Totally transcendental structures; 5.7 Interpreting groups and fields; History and bibliography; 6 The first-order case: compactness; 6.1 Compactness for first-order logic; 6.2 Boolean algebras and stone spaces; 6.3 Types; 6.4 Elementary amalgamation; 6.5 Amalgamation and preservation; 6.6 Expanding the language; 6.7 Stability; History and bibliography; 7 The countable case; 7.1 Fraisse's construction; 7.2 Omitting types; 7.3 Countable categoricity; 7.4 Cocategorical structures by fraisse's method History and bibliography8 The existential case; 8.1 Existentially closed structures; 8.2 Two methods of construction; 8.3 Model-completeness; 8.4 Quantifier elimination revisited; 8.5 More on e.c. models; 8.6 Amalgamation revisited; History and bibliography; 9 The Horn case: products; 9.1 Direct products; 9.2 Presentations; 9.3 Word-constructions; 9.4 Reduced products; 9.5 Ultraproducts; 9.6 The feferman-vaught theorem; 9.7 Boolean powers; History and bibliography; 10 Saturation; 10.1 The great and the good; 10.2 Big models exist; 10.3 Syntactic characterisations; 10.4 Special models 10.5 Definability10.6 Resplendence; 10.7 Atomic compactness; History and bibliography; 11 Combinatorics; 11.1 Indiscernibles; 11.2 Ehrenfeucht-Mostowski models; 11.3 Em models of unstable theories; 11.4 Nonstandard methods; 11.5 Defining well-orderings; 11.6 Infinitary indiscernibles; History and bibliography; 12 Expansions and categoricity; 12.1 One-cardinal and two-cardinal theorems; 12.2 Categoricity; 12.3 Cohomology of expansions; 12.4 Counting Expansions; 12.5 Relative categoricity; History and bibliography; Appendix: Examples; A.1 Modules; A.2 Abelian groups English. Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Théorie des modèles. MATHEMATICS General. bisacsh Model theory fast Modelltheorie gnd http://d-nb.info/gnd/4114617-7 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Wiskundige modellen. gtt Lógica matemática. larpcal Teoria dos modelos. larpcal Modelos matemáticos. larpcal Modèles, théorie des. ram Print version: Hodges, Wilfrid. Model theory 0521304423 (DLC) 91025082 (OCoLC)24173886 Encyclopedia of mathematics and its applications ; v. 42. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569376 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569376 Volltext |
| spellingShingle | Hodges, Wilfrid Model theory / Encyclopedia of mathematics and its applications ; Cover; Half-title; Encyclopedia of mathematics and its applications; Title; Copyright; Contents; Introduction; Note on notation; 1 Naming of parts; 1.1 Structures; 1.2 Homomorphisms and substructures; 1.3 Terms and atomic formulas; 1.4 Parameters and diagrams; 1.5 Canonical models; History And Bibliography; 2 Classifying structures; 2.1 Definable subsets; 2.2 Definable classes of structures; 2.3 Some notions from logic; 2.4 Maps and the formulas they preserve; 2.5 Classifying maps by formulas; 2.6 Translations; 2.7 Quantifier elimination; 2.8 Further examples; History and bibliography 3 Structures that look alike3.1 Theorems of skolem; 3.2 Back-and-forth equivalence; 3.3 Games for elementary equivalence; 3.4 Closed games; 3.5 Games and infinitary languages; 3.6 Clubs; History and bibliography; 4 Automorphisms; 4.1 Automorphisms; 4.2 Subgroups of small index; 4.3 Imaginary elements; 4.4 Eliminating imaginaries; 4.5 Minimal sets; 4.6 Geometries; 4.7 Almost strongly minimal theories; 4.8 Zil'ber's configuration; History and bibliography; 5 Interpretations; 5.1 Relativisation; 5.2 Pseudo-elementary Classes; 5.3 Interpreting one structure in another 5.4 Shapes and sizes of interpretations5.5 Theories that interpret anything; 5.6 Totally transcendental structures; 5.7 Interpreting groups and fields; History and bibliography; 6 The first-order case: compactness; 6.1 Compactness for first-order logic; 6.2 Boolean algebras and stone spaces; 6.3 Types; 6.4 Elementary amalgamation; 6.5 Amalgamation and preservation; 6.6 Expanding the language; 6.7 Stability; History and bibliography; 7 The countable case; 7.1 Fraisse's construction; 7.2 Omitting types; 7.3 Countable categoricity; 7.4 Cocategorical structures by fraisse's method History and bibliography8 The existential case; 8.1 Existentially closed structures; 8.2 Two methods of construction; 8.3 Model-completeness; 8.4 Quantifier elimination revisited; 8.5 More on e.c. models; 8.6 Amalgamation revisited; History and bibliography; 9 The Horn case: products; 9.1 Direct products; 9.2 Presentations; 9.3 Word-constructions; 9.4 Reduced products; 9.5 Ultraproducts; 9.6 The feferman-vaught theorem; 9.7 Boolean powers; History and bibliography; 10 Saturation; 10.1 The great and the good; 10.2 Big models exist; 10.3 Syntactic characterisations; 10.4 Special models 10.5 Definability10.6 Resplendence; 10.7 Atomic compactness; History and bibliography; 11 Combinatorics; 11.1 Indiscernibles; 11.2 Ehrenfeucht-Mostowski models; 11.3 Em models of unstable theories; 11.4 Nonstandard methods; 11.5 Defining well-orderings; 11.6 Infinitary indiscernibles; History and bibliography; 12 Expansions and categoricity; 12.1 One-cardinal and two-cardinal theorems; 12.2 Categoricity; 12.3 Cohomology of expansions; 12.4 Counting Expansions; 12.5 Relative categoricity; History and bibliography; Appendix: Examples; A.1 Modules; A.2 Abelian groups Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Théorie des modèles. MATHEMATICS General. bisacsh Model theory fast Modelltheorie gnd http://d-nb.info/gnd/4114617-7 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Wiskundige modellen. gtt Lógica matemática. larpcal Teoria dos modelos. larpcal Modelos matemáticos. larpcal Modèles, théorie des. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85086421 http://d-nb.info/gnd/4114617-7 http://d-nb.info/gnd/4037951-6 |
| title | Model theory / |
| title_auth | Model theory / |
| title_exact_search | Model theory / |
| title_full | Model theory / Wilfrid Hodges. |
| title_fullStr | Model theory / Wilfrid Hodges. |
| title_full_unstemmed | Model theory / Wilfrid Hodges. |
| title_short | Model theory / |
| title_sort | model theory |
| topic | Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Théorie des modèles. MATHEMATICS General. bisacsh Model theory fast Modelltheorie gnd http://d-nb.info/gnd/4114617-7 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Wiskundige modellen. gtt Lógica matemática. larpcal Teoria dos modelos. larpcal Modelos matemáticos. larpcal Modèles, théorie des. ram |
| topic_facet | Model theory. Théorie des modèles. MATHEMATICS General. Model theory Modelltheorie Mathematische Logik Wiskundige modellen. Lógica matemática. Teoria dos modelos. Modelos matemáticos. Modèles, théorie des. |
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| work_keys_str_mv | AT hodgeswilfrid modeltheory |