Hechler's theorem for the null ideal

Details Hechler's theorem for the null ideal Hechler's theorem for the null ideal

2002-11-15

arxiv.org/abs/math/0211244v8

Arch. Math. Logic, Vol. 43(2004), pp. 703--722.

Mathematics

Logic

v8: Minor corrections

Scientific paper

10.1007/s00153-004-0224-4

We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler's classical result in the theory of forcing, and the statement of the theorem for the meager ideal has been already proved by Bartoszynski and the author.

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