This is one of two articles that came out of my dissertation (also titled The Ground Axiom).
The Ground Axiom
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Dissertation: The Ground Axiom
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Unforcing and the Ground Axiom My interest in “unforcing,” somehow working backwards from a forcing extension to a ground model, started early in my set theory studies. When I went through the rite of passage of learning Paul Cohen’s forcing – an exercise in induction, with a lovely (and at the time, frustratingly opaque) back-and-forth between technical details and...
Inner-Model Reflection Principles
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This paper has its origins in a question by Neil Barton on Math.SE, “What is the consistency strength of width-reflection?” Start with one of the foundational relationships of set theory, that of height-reflection — any property true in the universe $V$ is true in some initial segment $V_\kappa$. Then “rotate your head ninety degrees” and consider the corresponding...
