James E. Hanson

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math.LO2026

A formula for any real number, maybe

James E. Hanson, Connor Watson

We discuss how to write down three specific natural numbers $A$ , $B$ , $C$ such that for any real number $r$ you've probably ever thought of, it is consistent with $ZFC$ se…

math.LO2025

Labelled growth rates of $ω$ -categorical structures and applications in choiceless set theory

Bertalan Bodor, Samuel Braunfeld, James E. Hanson

We study the labelled growth rate of an $ω$ -categorical structure $A$ , i.e., the number of orbits of $A u t (A)$ on $n$ -tuples of distinct elements, and show tha…

math.LO2025

A combinatorial characterization of Kim's lemma for pairs of bi-invariant types

James E. Hanson

We give a combinatorial consistency-inconsistency configuration that is equivalent to the failure of the following form of Kim's lemma for a given $k$ : $(⋆)$ For any set of par…

math.LO2025

Any function I can actually write down is measurable, right?

James E. Hanson

In this expository paper aimed at a general mathematical audience, we discuss how to combine certain classic theorems of set-theoretic inner model theory and effective descriptive…

A formula for any real number, maybe

Labelled growth rates of ω-categorical structures and applications in choiceless set theory

A combinatorial characterization of Kim's lemma for pairs of bi-invariant types

Any function I can actually write down is measurable, right?

Labelled growth rates of $ω$ -categorical structures and applications in choiceless set theory