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A coding theorem for measures

Kechris, Alexander S. (1988) A coding theorem for measures. In: Cabal Seminar 81–85. Lectures Notes in Mathematics. No.1333. Springer , Berlin, pp. 103-109. ISBN 978-3-540-50020-9.

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Assuming ZF + DC + AD Moschovakis (see [Ml]) has shown that if there is a surjection π : R → λ from the reals (R = ω^ω in this paper) onto an ordinal λ, then there is a surjection π^* : R → p(λ) from the reals onto the power set of λ. Let us denote by β(λ) the set of ultrafilters on λ. The question was raised whether there is an analog of Moschovakis' Theorem for β(λ), i.e. if there is a surjection from R onto λ, is there one from R onto β(λ)? Martin showed that this cannot be proved in ZF + DC + AD alone because if V = L(R) and λ= ol, there is no surjection of R onto β(λ).

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Additional Information:© 1988 Springer. Research partially supported by NSF Grants MCS-8117804 and DMS-8416349.
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MathSciNet ReviewMR0960898
Series Name:Lectures Notes in Mathematics
Issue or Number:1333
Record Number:CaltechAUTHORS:20130612-074122964
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Official Citation:A coding theorem for measures Alexander S. Kechris Pages 103-109
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38899
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2013 15:11
Last Modified:09 Nov 2021 23:40

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