Lectures on infinitary model theory:
Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathemat...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2016
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| Schriftenreihe: | Lecture notes in logic
46 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBY01 URL des Erstveröffentlichers |
| Zusammenfassung: | Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 08 Aug 2016) |
| Beschreibung: | 1 online resource (viii, 183 pages) |
| ISBN: | 9781316855560 |
| DOI: | 10.1017/CBO9781316855560 |
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| 520 | |a Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory | ||
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Datensatz im Suchindex
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| author | Marker, D. 1958- |
| author_facet | Marker, D. 1958- |
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| author_sort | Marker, D. 1958- |
| author_variant | d m dm |
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| 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 |
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| format | Electronic eBook |
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| id | DE-604.BV043940094 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:12Z |
| institution | BVB |
| isbn | 9781316855560 |
| language | English |
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| physical | 1 online resource (viii, 183 pages) |
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| series2 | Lecture notes in logic |
| spelling | Marker, D. 1958- Verfasser aut Lectures on infinitary model theory David Marker Cambridge Cambridge University Press 2016 1 online resource (viii, 183 pages) txt rdacontent c rdamedia cr rdacarrier Lecture notes in logic 46 Title from publisher's bibliographic system (viewed on 08 Aug 2016) Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory Infinitary languages Logic Deskriptive Mengenlehre (DE-588)4149180-4 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Rekursionstheorie (DE-588)4122329-9 gnd rswk-swf Modelltheorie (DE-588)4114617-7 s Rekursionstheorie (DE-588)4122329-9 s Deskriptive Mengenlehre (DE-588)4149180-4 s Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 Erscheint auch als Druckausgabe 978-1-107-18193-9 https://doi.org/10.1017/CBO9781316855560 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Marker, D. 1958- Lectures on infinitary model theory Infinitary languages Logic Deskriptive Mengenlehre (DE-588)4149180-4 gnd Mathematische Logik (DE-588)4037951-6 gnd Modelltheorie (DE-588)4114617-7 gnd Rekursionstheorie (DE-588)4122329-9 gnd |
| subject_GND | (DE-588)4149180-4 (DE-588)4037951-6 (DE-588)4114617-7 (DE-588)4122329-9 |
| title | Lectures on infinitary model theory |
| title_auth | Lectures on infinitary model theory |
| title_exact_search | Lectures on infinitary model theory |
| title_full | Lectures on infinitary model theory David Marker |
| title_fullStr | Lectures on infinitary model theory David Marker |
| title_full_unstemmed | Lectures on infinitary model theory David Marker |
| title_short | Lectures on infinitary model theory |
| title_sort | lectures on infinitary model theory |
| topic | Infinitary languages Logic Deskriptive Mengenlehre (DE-588)4149180-4 gnd Mathematische Logik (DE-588)4037951-6 gnd Modelltheorie (DE-588)4114617-7 gnd Rekursionstheorie (DE-588)4122329-9 gnd |
| topic_facet | Infinitary languages Logic Deskriptive Mengenlehre Mathematische Logik Modelltheorie Rekursionstheorie |
| url | https://doi.org/10.1017/CBO9781316855560 |
| work_keys_str_mv | AT markerd lecturesoninfinitarymodeltheory |