On Russell typicality in Set Theory
Logic
2021-11-16 v1
Abstract
By Tzouvaras, a set is nontypical in the Russell sense, if it belongs to a countable ordinal definable set. The class HNT of all hereditarily nontypical sets satisfies all axioms of ZF and the double inclusion HODHNTV holds. Several questions about the nature of such sets, recently proposed by Tzouvaras, are solved in this paper. In particular, a model of ZFC is presented in which HODHNTV, and another model of ZFC, in which HNT does not satisfy the axiom of choice.
Keywords
Cite
@article{arxiv.2111.07654,
title = {On Russell typicality in Set Theory},
author = {Vladimir Kanovei and Vassily Lyubetsky},
journal= {arXiv preprint arXiv:2111.07654},
year = {2021}
}