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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