On the classification of definable ccc forcing notions

Mohammad Golshani; Haim Horowitz; Saharon Shelah

On the classification of definable ccc forcing notions

Logic 2023-01-03 v2

Authors: Mohammad Golshani , Haim Horowitz , Saharon Shelah

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.

Keywords

set theory forcing set theory

Cite

@article{arxiv.1610.07553,
  title  = {On the classification of definable ccc forcing notions},
  author = {Mohammad Golshani and Haim Horowitz and Saharon Shelah},
  journal= {arXiv preprint arXiv:1610.07553},
  year   = {2023}
}

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This is publication 1097 of the third author

On the classification of definable ccc forcing notions

Abstract

Keywords

Cite

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