## 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.

### MSC:

 3e+35 Consistency and independence results

### Keywords:

Hechler’s theorem; Forcing; Meager ideal
Full Text:

### References:

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