Nicely generated and chaotic ideals

We show that if the real line is the disjoint union of $\kappa$ meager sets such that every meager set is contained in a countable union of them, then $\kappa = \omega _1$. This answers a question addressed by Jacek Cicho\'{n}. We also prove two theorems saying roughly that any attempt to produce 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.