Mathematical Research Letters

Volume 11 (2004)

Number 5

Between Maharam’s and von Neumann’s problems

Pages: 673 – 684

DOI: http://dx.doi.org/10.4310/MRL.2004.v11.n5.a10

Authors

Ilijas Farah (York University)

Jindrich Zapletal (University of Florida)

Abstract

In the context of definable algebras Maharam’s and von Neumann’s problems essentially coincide. Consequently, random forcing is the only definable ccc forcing adding a single real that does not make the ground model reals null, and the only pairs of definable ccc $\sigma$-ideals with the Fubini property are $(\mathtt{meager},\mathtt{meager})$ and $(\mathtt{null},\mathtt{null})$.

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