6 papers
A natural haystack of differentially closed fields
James E. Hanson
In this partially expository paper, we present a novel construction of differentially closed fields of characteristic : Let be the differential ri…
The Countable Reals
Andrej Bauer, James E. Hanson
We construct a topos in which the Dedekind reals are countable. The topos arises from a new kind of realizability, which we call parameterized realizability, based on partial combi…
A formula for any real number, maybe
James E. Hanson, Connor Watson
We discuss how to write down three specific natural numbers , , such that for any real number you've probably ever thought of, it is consistent with se…
Labelled growth rates of -categorical structures and applications in choiceless set theory
Bertalan Bodor, Samuel Braunfeld, James E. Hanson
We study the labelled growth rate of an -categorical structure , i.e., the number of orbits of on -tuples of distinct elements, and show th…
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 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 : For any set of par…