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arXiv · 1610.07553

On the classification of definable ccc forcing notions

Mohammad Golshani·Haim Horowitz·Saharon Shelah
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Abstract

We show that for a Suslin ccc forcing notion $\mathbb Q$ adding a Hechler real, ``$\text{ZF}+\text{DC}_{\omega_1}+$all sets of reals are $I_{\mathbb Q,\aleph_0}$-measurable'' implies the existence of an inner model with a measurable cardinal. We also introduce a wide class of Suslin ccc forcing notions which add a Hechler real, so that the above result applies to them.

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Mohammad Golshani, Haim Horowitz, Saharon Shelah. 2016-10-24. On the classification of definable ccc forcing notions. https://arxiv.org/abs/1610.07553

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