11 citations · 16 across the 12 of their papers we have counts for
6 papers · 1 filter
Elementary topoi
Jordan Mitchell Barrett
As the prototypical category, has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $…
The reverse mathematics of Cousin's lemma
Jordan Mitchell Barrett
Cousin's lemma is a compactness principle that naturally arises when studying the gauge integral, a generalisation of the Lebesgue integral. We study the axiomatic strength of Cous…
On Ramsey-minimal infinite graphs
Jordan Mitchell Barrett, Valentino Vito
For fixed finite graphs , , a common problem in Ramsey theory is to study graphs such that , i.e. every red-blue coloring of the edges of produces either…
Random tree-weighted graphs
Louigi Addario-Berry, Jordan Barrett
For each , let be a sequence of positive integers with even sum . Let be uniformly dist…
Ramsey theory for layered semigroups
Jordan Mitchell Barrett
We further develop the theory of layered semigroups, as introduced by Farah, Hindman and McLeod, providing a general framework to prove Ramsey statements about such a semigroup …
On functor-quotients and their isomorphism theorems
Jordan Mitchell Barrett, Valentino Vito
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more gene…