Hechler’s theorem for the null ideal. (English) Zbl 1057.03039

Summary: We prove the following theorem: For a partially ordered set \(Q\) such that every countable subset of \(Q\) has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, 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. The corresponding theorem for the meager ideal was established by Bartoszyński and Kada.


03E35 Consistency and independence results
03E17 Cardinal characteristics of the continuum
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