Reference to a "simple" consistency proof

Question

Bartoszynski has written a "simplified" account of Shelah's proof of consistency of "Covering of null ideal has countable cofinality" in his article in handbook. In a subsequent paper, Shelah also constructed a model of "The null ideal restricted to some non null set is $\omega_1$-saturated". The proof uses iterations of "partial random reals" and makes several references to his countable cofinality paper and I could not follow it starting page 17. Has someone written a simplified account of this proof that maybe does not refer to Shelah's countable cofinality paper?

Answer 1

Shelah and I have a preprint that has a generalization of this. The main result is that the null ideal restricted to a non null set of reals could be isomorphic to a large class of sigma ideals - For example it could be isomorphic to the non stationary ideal on $\omega_1$.