Kechris, Alexander S. (1985) Determinacy and the Structure of L(R). In: Recursion Theory. Proceedings of Symposia in Pure Mathematics. No.42. American Mathematical Society , Providence, RI, pp. 271283. ISBN 9780821814475. http://resolver.caltech.edu/CaltechAUTHORS:20130611130509199

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Abstract
Let ω = {0, 1, 2, ... } be the set of natural numbers and R = ω^ω the set of all infinite sequences from ω, or for simplicity reals. To each set A ⊆ R we associate a twoperson infinite game, in which players I and II alternatively play natural numbers I x(0) x(2) II x(1) x(3)...x(O), x(l), x(2), ... and if x is the real they eventually produce, then I wins iff x є A. The notion of a winning strategy for player I or II is defined in the usual way, and we call A determined if either player I or player II has a winning strategy in the above game. For a collection ⌈ of sets of reals let ⌈DET be the statement that all sets A є ⌈ are determined. Finally AD (The Axiom of Determinacy) is the statement that all sets of reals are determined.
Item Type:  Book Section  

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Additional Information:  © 1985 American Mathematical Society. Research partially supported by NSF Grant MCS8117804  
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Classification Code:  1980 MSC: Primary 03E47, 90D05, 90D13  
Record Number:  CaltechAUTHORS:20130611130509199  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20130611130509199  
Official Citation:  Alexander S. Kechris – Determinacy and the structure of L(R) Chapter III Pages: 271283  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  38892  
Collection:  CaltechAUTHORS  
Deposited By:  Ruth Sustaita  
Deposited On:  11 Jun 2013 20:47  
Last Modified:  11 Jun 2013 20:47 
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