Nicely generated and chaotic ideals

Details Nicely generated and chaotic ideals Nicely generated and chaotic ideals

1994-07-17

arxiv.org/abs/math/9407208v1

Mathematics

Logic

Scientific paper

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.

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