Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 1988 | public
Book Section - Chapter

A coding theorem for measures

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).

Additional Information

© 1988 Springer. Research partially supported by NSF Grants MCS-8117804 and DMS-8416349.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024