UID:
almahu_9949462249202882
Format:
1 online resource (317 p.) :
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Zahlr. Abb.
Edition:
Reprint 2015
ISBN:
9783110200065
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9783110238570
Series Statement:
De Gruyter Series in Logic and Its Applications , 7
Content:
In diesem Band entwickelt und verwendet der Autor Verfahren, um - ausgehend von großen Kardinalzahlen - die Determiniertheit von definierbaren Spielen mit abzählbarer Länge auf natürlichen Zahlen nachzuweisen. Die Determiniertheit ist letztlich abgeleitet von Iterationsstrategien, die Spiele auf natürlichen Zahlen mit den spezifischen iterativen Spielen verbinden, die bei der Untersuchung großer Kardinalzahlen aufkommen.
Content:
In this volume the author develops and applies methods for proving, from large cardinals, the determinacy of definable games of countable length on natural numbers. The determinacy is ultimately derived from iteration strategies, connecting games on natural numbers with the specific iteration games that come up in the study of large cardinals. The games considered in this text range in strength, from games of fixed countable length, through games where the length is clocked by natural numbers, to games in which a run is complete when its length is uncountable in an inner model (or a pointclass) relative to the run. More can be done using the methods developed here, reaching determinacy for games of certain length. The book is largely self-contained. Only graduate level knowledge of modern techniques in large cardinals and basic forcing is assumed. Several exercises allow the reader to build on the results in the text, for example connecting them with universally Baire and homogeneously Suslin sets. - Important contribution to one of the main features of current set theory, as initiated and developed by Jensen, Woodin, Steel and others.
Note:
Frontmatter --
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Contents --
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Introduction --
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Chapter 1 Basic components --
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Chapter 2 Games of fixed countable length --
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Chapter 3 Games of continuously coded --
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length --
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Chapter 4 Pullbacks --
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Chapter 5 When both players lose --
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Chapter 6 Along a single branch --
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Chapter 7 Games which reach local cardinals --
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Backmatter
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Issued also in print.
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Mode of access: Internet via World Wide Web.
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In English.
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2008, De Gruyter, 9783110212129
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008, De Gruyter, 9783110212136
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008, De Gruyter, 9783110209082
Additional Edition:
ISBN 9783110183412
Language:
English
Subjects:
Mathematics
DOI:
10.1515/9783110200065
URL:
https://doi.org/10.1515/9783110200065
URL:
https://www.degruyter.com/isbn/9783110200065
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