Forcings with ideals and simple forcing notions

Using generic ultrapower techniques we prove the following statements: (1) for every sequence 〈μ _n |n <ω〉 of 0-1 σ-additive measures over the set of reals, there exists a set which is nonmeasurable in each μ _n, (2) there is no nowhere prime σ-complete א₀-dense ideal, (3) if I is a nowhere prime ideal over a set X then add (I) ≦d(I), (4) suppose that μ is a σ-additive total nowhere prime probability measure over a set X, then add (μ) <d(μ), in particular, if μ is a real valued measure on the continuum, then the measure algebra cannot have countable density, (5) there is no σ-complete ideal I over a set X such that the forcing with I is isomorphic to the Cohen real forcing or to the random real forcing or to the Hechler real forcing or to the Sacks real forcing. Some general conditions on forcing preventing it for being isomorphic to the forcing with an ideal are formulated.