NICELY GENERATED AND CHAOTIC IDEALS

We show that if the real line is the disjoint union of kappa meager se ts such that every meager set is contained in a countable union of the m, then kappa = omega(1). This answers a question addressed by Jacek C ichon. We also prove two theorems saying roughly that any attempt to p roduce the isomorphism type of the meager ideal in the Cohen real and the random real extensions must fail. All our results hold for meager replaced by null, as well.