  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.
