The Determinacy of Long Games by Itay Neeman ISBN 3110183412 978-3110183412
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Product details:
ISBN 10: 3110183412
ISBN 13: 978-3110183412
Author: Itay Neeman
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.
Table of contents:
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
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