# Sh:1097

• Horowitz, H., & Shelah, S. On the classification of definable ccc forcing notions. Preprint. arXiv: 1610.07553
• Abstract:
We show that for a Suslin ccc forcing notion \mathbb Q adding a Hechler real, ZF+DC_{\omega_1}+"All sets of reals are I_{\mathbb 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.
• Version 2020-06-03 (18p)
Bib entry
@article{Sh:1097,
author = {Horowitz, Haim and Shelah, Saharon},
title = {{On the classification of definable ccc forcing notions}},
note = {\href{https://arxiv.org/abs/1610.07553}{arXiv: 1610.07553}},
arxiv_number = {1610.07553}
}