Dissertations, Theses, and Capstone Projects
Date of Degree
6-2017
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Gunter Fuchs
Committee Members
Joel David Hamkins
Arthur Apter
Keywords
Logic, Set Theory, Forcing
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 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 ω1-trees, preservation properties of subcomplete forcing, the subcomplete maximality principle, the subcomplete resurrection axiom, and show that diagonal Prikry forcing is subcomplete.
Recommended Citation
Minden, Kaethe B., "On Subcomplete Forcing" (2017). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/2120