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Cover: 9781848904231 | Classification Theory. Second Edition with a new introduction | Shelah
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Classification Theory. Second Edition with a new introduction
Taschenbuch von Saharon Shelah
Sprache: Englisch

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Beschreibung
This book is for readers who have learned about first order logic; Gödel's completeness theorem; the Löwenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones.

The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.
This book is for readers who have learned about first order logic; Gödel's completeness theorem; the Löwenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones.

The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.
Details
Erscheinungsjahr: 2023
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9781848904231
ISBN-10: 1848904231
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Shelah, Saharon
Hersteller: College Publications
Maße: 234 x 156 x 40 mm
Von/Mit: Saharon Shelah
Erscheinungsdatum: 13.01.2023
Gewicht: 1,115 kg
Artikel-ID: 126508780
Details
Erscheinungsjahr: 2023
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9781848904231
ISBN-10: 1848904231
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Shelah, Saharon
Hersteller: College Publications
Maße: 234 x 156 x 40 mm
Von/Mit: Saharon Shelah
Erscheinungsdatum: 13.01.2023
Gewicht: 1,115 kg
Artikel-ID: 126508780
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