The Determinacy of Long Games - Neeman, Itay
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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…mehr

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Produktbeschreibung
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.
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.
Autorenporträt
Itay Neeman is Professorat the Mathematics Department of the University of California at Los Angeles, California, USA.
Rezensionen
"There is an excellent extensive Introduction presenting a view of the theory that can be profitable for a non-specialist as well."
(ap) in: EMS-Newsletter 3/2007

"For the intended audience, this is an enjoyable book, written in the author's delectable and clear style of mathematics." Mathematical Reviews