On Subcomplete Forcing

Kaethe Minden

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arXiv · 1705.00386

On Subcomplete Forcing

Kaethe Minden

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Abstract

I survey an array of topics in set theory in the context of a novel class of forcing notions: subcomplete forcing. Subcompleteness was originally defined by Ronald Jensen. I have attempted to make the subject somewhat more approachable to set theorists, while showing various properties of subcomplete forcing which one might desire of a forcing class, drawing comparisons between subcomplete forcing and countably closed forcing. In particular, I look at the interaction between subcomplete forcing and $\omega_1$-trees, preservation properties of subcomplete forcing, the subcomplete maximality principle, the subcomplete resurrection axiom, and show that generalized diagonal Prikry forcing is subcomplete.

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BibTeX RIS

Kaethe Minden. 2017-04-30. On Subcomplete Forcing. https://arxiv.org/abs/1705.00386

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