The Determinacy of Long Games

Itay Neeman

Published by De Gruyter 2004

The Determinacy of Long Games

Itay Neeman

Volume 7 in the series De Gruyter Series in Logic and Its Applications

https://doi.org/10.1515/9783110200065

Overview
Contents

About this book

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.

Author / Editor information

Itay Neeman is Professor at the Mathematics Department of the University of California at Los Angeles, California, USA.

Reviews

"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

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Contents Requires Authentication Unlicensed Licensed Download PDF	ix
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 1 Basic components Requires Authentication Unlicensed Licensed Download PDF	15
Chapter 2 Games of fixed countable length Requires Authentication Unlicensed Licensed Download PDF	51
Chapter 3 Games of continuously coded length Requires Authentication Unlicensed Licensed Download PDF	87
Chapter 4 Pullbacks Requires Authentication Unlicensed Licensed Download PDF	135
Chapter 5 When both players lose Requires Authentication Unlicensed Licensed Download PDF	175
Chapter 6 Along a single branch Requires Authentication Unlicensed Licensed Download PDF	209
Chapter 7 Games which reach local cardinals Requires Authentication Unlicensed Licensed Download PDF	268
Backmatter Requires Authentication Unlicensed Licensed Download PDF	301

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: Reprint 2015
Audience: Research Mathematicians, in particular set Theorists; Advanced Graduate Students; Theoretical Computer Scientists; Academic Libraries
Pages
- Front matter: 11
- Main content: 317
Illustrations
- Other: Zahlr. Abb.
Keywords: Determiniertheit; Große Kardinalzahlen; Unendliche Spiele; Spieltheorie; Mengenlehre

eBook

Published: August 22, 2008
ISBN: 9783110200065

Hardcover

Published: November 24, 2004
ISBN: 9783110183412