On possible restrictions of the null ideal

by Kumar and Shelah. [KmSh:1102]

We prove that the null ideal restricted to a non null set of reals could be isomorphic to a variety of sigma ideals. Using this, we show that the following are consistent: (1) There is a non null subset of plane each of whose non null subsets contains three collinear points. (2) There is a partition of a non null set of reals into null sets, each of size aleph_1, such that every transversal of this partition is null.

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