On the classification of definable ccc forcing notions

2016/10/24 by Mohammad Golshani, Golshani, Mohammad, Haim Horowitz +3
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1610.07553

openalex publication_date 2016/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for a Suslin ccc forcing notion \mathbb Q adding a Hechler real, ``ZF+DC_ω1+all sets of reals are I_{\mathbb Q,ℵ0}-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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