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. http://resolver.caltech.edu/CaltechAUTHORS:20130612-074122964
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Abstract
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).
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 1988 Springer. Research partially supported by NSF Grants MCS-8117804 and DMS-8416349. | |||||||||
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| Record Number: | CaltechAUTHORS:20130612-074122964 | |||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20130612-074122964 | |||||||||
| 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 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 12 Jun 2013 15:11 | |||||||||
| Last Modified: | 12 Jun 2013 15:11 |
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