Combinatorial Properties of the Raisonnier Filter
Logic
2026-02-27 v1
Abstract
The Raisonnier Filter is a combinatorial object isolated by Jean Raisonnier in order to simplify Shelah's proof that if all sets are Lebesgue-measurable then there is an inner model with an inaccessible cardinal. In this paper, we study the combinatorics of a general version of the Raisonnier filter, with an eye to potential applications in descriptive set theory. Among the most interesting of our results is a partial converse to Raisonnier's theorem, which can be used to provide a new characterisation of the statement "all sets are measurable". We also introduce an ideal on the Cantor Space induced by the Raisonnier filter and study its cardinal characteristics, connecting them to the well-known characteristics in Cicho\'n's Diagram.
Keywords
Cite
@article{arxiv.2602.23340,
title = {Combinatorial Properties of the Raisonnier Filter},
author = {Spyridon Dialiatsis and Yurii Khomskii},
journal= {arXiv preprint arXiv:2602.23340},
year = {2026}
}