3 papers
math.LO2026
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…
math.LO2026
The transcendence degree of the reals over certain set-theoretical subfields
Azul Fatalini, Ralf Schindler
It is a well-known result that, after adding one Cohen real, the transcendence degree of the reals over the ground-model reals is continuum. We extend this result for a set of…
math.LO2025
Partitions of into unit circles with no well-ordering of the reals
Azul Fatalini
Using a well-ordering on the reals, one can prove there exists a partition of the three-dimensional Euclidean space into unit circles (PUC). We show that the converse does not hold…