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Determinacy and the Structure of L(R)

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. 271-283. ISBN 978-0-8218-1447-5.

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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 two-person 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 MCS81-17804
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MathSciNet ReviewMR0791063
Series Name:Proceedings of Symposia in Pure Mathematics
Issue or Number:42
Classification Code:1980 MSC: Primary 03E47, 90D05, 90D13
Record Number:CaltechAUTHORS:20130611-130509199
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Official Citation:Alexander S. Kechris – Determinacy and the structure of L(R) Chapter III Pages: 271-283
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38892
Deposited By: Ruth Sustaita
Deposited On:11 Jun 2013 20:47
Last Modified:09 Nov 2021 23:40

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