Cohen forcing and inner models, (2020). Math. Log. Quart., 66: 65-72. doi:10.1002/malq.201800062, arXiv Inner mantles and iterated HOD, with Kameryn J. Williams, (2019), . Math. Log. Quart., 65: 498-510. doi:10.1002/malq.201800071.  arXiv Inner-model reflection principles, with Neil Barton, Andres Caicedo, Gunter Fuchs, Joel David Hamkins and Ralf Schindler, Stud. Logica (2019). ; pdf, arXiv...

Dissertation: The Ground Axiom

Cracked earth

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

A lit up object sitting on top of a table

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...

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