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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.

MSC:

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