Boolean Algebras of the family of subsets of reals modulo meagre or null

@inproceedings{Shelah1994BooleanAO,
  title={Boolean Algebras of the family of subsets of reals modulo meagre or null},
  author={Saharon Shelah},
  year={1994}
}
We prove that any Souslin c.c.c. forcing notion which add a non dominated real add a Cohen real. We also prove that any Souslin c.c.c. forcing add a real which is not on any old narrow tree. The feeling that those two forcing notions -Cohen and Random(equivalently the corresponding Boolean algebras P(R)/(meagre sets), P(R)/(null sets)) are special, was probably old and widespread. A reasonable interpretation is to show them unique, or “minimal” or at least characteristic in a family of “nice… CONTINUE READING