3 citations · 3 across the 1 of their papers we have counts for
9 papers
Analyticity for rapidly determined properties of Poisson Galton--Watson trees
Yuval Peres, Andrew Swan
Let be a Galton--Watson tree with Poisson() offspring, and let be a tree property. In this paper, are concerned with the regularity of the function $\mathbb{P}_λ(A):=…
On Church's Thesis in Cubical Assemblies
Andrew Swan, Taichi Uemura
We show that Church's thesis, the axiom stating that all functions on the naturals are computable, does not hold in the cubical assemblies model of cubical type theory. We show tha…
Identity Types in Algebraic Model Structures and Cubical Sets
Andrew Swan
We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct mann…
Separating Path and Identity Types in Presheaf Models of Univalent Type Theory
Andrew Swan
We give a collection of results regarding path types, identity types and univalent universes in certain models of type theory based on presheaves. The main result is that path type…
On Dividing by Two in Constructive Mathematics
Andrew Swan
A classic result due to Bernstein states that in set theory with classical logic, but without the axiom of choice, for all sets and , if then a…
W-Types with Reductions and the Small Object Argument
Andrew Swan
We define a simple kind of higher inductive type generalising dependent -types, which we refer to as -types with reductions. Just as dependent -types can be characterised…