  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 J. Cichon. 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.
