Hechler’s theorem for the meager ideal. (English) Zbl 1059.03049

Summary: 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 meager 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.


03E35 Consistency and independence results
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