The Determinacy of Long Games / / Itay Neeman.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Neeman, Itay,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2008]; ©2004
• Year of Publication: 2008
• Edition: Reprint 2015
• Language: English
• Series: De Gruyter Series in Logic and Its Applications , 7
• Physical Description: 1 online resource (317 p.) :; Zahlr. Abb.
• Other title: Frontmatter --; Contents --; Introduction --; Chapter 1 Basic components --; Chapter 2 Games of fixed countable length --; Chapter 3 Games of continuously coded --; length --; Chapter 4 Pullbacks --; Chapter 5 When both players lose --; Chapter 6 Along a single branch --; Chapter 7 Games which reach local cardinals --; Backmatter
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110200065; 9783110238570; 9783110238471; 9783110637205; 9783110212129; 9783110212136; 9783110209082
• ISSN: 1438-1893
• DOI: 10.1515/9783110200065
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Itay Neeman.

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. 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.