5 papers · 1 filter
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 $…
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…
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 indepen…
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, Transversals, and the Hat Game
Luke Serafin
Geschke, Lubarsky, and Rahn in ``Choice and the Hat Game''~\cite{choice-and-the-hat-game} generalize the classic hat game puzzle to infinitely-many players and ask whether every mo…