5 papers
Projective Chromatic Numbers
Adrian Rettich, Luke Serafin
We extend classical notions of definable colourability of graphs to the general projective setting and investigate whether known results, mainly about the dichotomy and the $…
Morita Rigidity for Kleene Algebras
Luke Serafin
We introduce Morita equivalence to the study of Kleene algebras and modules. Classical characterizations of Morita-equivalent semirings such as having equivalent categories of modu…
Funicular preorders can be prelinearized without nonprincipal ultrafilters over
Azul Fatalini, Luke Serafin
It is a consequence of the axiom of choice that every preorder can be extended to a total preorder while respecting the strict preorder relation. We call such an extension a prelin…
On Strongly-equitable Social Welfare Orders Without the Axiom of Choice
Luke Serafin
Social welfare orders seek to combine the disparate preferences of an infinite sequence of generations into a single, societal preference order in some reasonably-equitable way. In…
Ultrafilters over Successor Cardinals and the Tukey Order
Tom Benhamou, Justin T. Moore, Luke Serafin
We study ultrafilters on regular uncountable cardinals, with a primary focus on , and particularly in relation to the Tukey order on directed sets. Results include the indepe…