Research

I research philosophical, historical, and mathematical questions having to do with set theory, especially descriptive set theory, set theory of the real line, choiceless large cardinals, foundations of mathematics, and mathematical practice.

philosophy

Justification by Confluence

What do we mean when we say we have a Church-Turing Thesis for something?

Metamathematical Methods in Descriptive Set Theory

A case study of the practice of classifying proofs by their methodology.

history

Emergence of Invariant Descriptive Set Theory

How and when did descriptive set theoreists come to study Borel equivalence relations?

mathematical logic

Computability relative to generic sets

If a set is computable using sufficiently random or generic information, then is it computable in the usual sense?