### On the classification of definable ccc forcing notions

by Horowitz and Shelah. [HwSh:1097]

We show that for a Suslin ccc forcing notion Q
adding a Hechler real, ZF+DC_{omega_1}+'' All sets of reals
are
I_Q, aleph_0-measurable'' implies the existence of
an inner model with a measurable cardinal. We also further
investigate
the forcing notions from {[}HwSh:1067{]}, showing that some
of
them
add Hechler reals (so the above result applies to them) while
others
don't add dominating reals.

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