ENGLISH

The Determinacy Of Long Games

By Itay Neeman

Book information

Publisher
Walter de Gruyter Inc
Year
2004
ISBN
3110183412, 9783110183412
Language
english
Format
PDF
Filesize
2 MB (1921442 bytes)
Series
De Gruyter Series in Logic and Its Applications
Pages
330\330
Topic
Mathematics Logic
Time added
2013-06-05 13:28:26

Description

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.

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