The null ideal restricted to some non-null set may be $\aleph _1$-saturated
Tom 179 / 2003
Fundamenta Mathematicae 179 (2003), 97-129 MSC: 03E35, 03E55, 03E19. DOI: 10.4064/fm179-2-1
Our main result is that possibly some non-null set of reals cannot be divided into uncountably many non-null sets. We also deal with a non-null set of real, the graph of any function from which is null, and deal with our iterations somewhat more generally.