2021/11/15 by Vladimir Kanovei, Kanovei, Vladimir, Vassily Lyubetsky +1 · 1 citation
Mathematics · #FOS: Mathematics #Logic (math.LO) #Primary 03E35 #math.LO #msc:03E15 #msc:03E35 #secondary 03E15
paper · pdf · doi:10.48550/arxiv.2111.07654
arxiv created 2021/11/15 · arxiv updated 2021/11/16
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 HOD⊆HNT⊆V 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 HOD\subsetneqqHNT\subsetneqqV, and another model of ZFC, in which HNT does not satisfy the axiom of choice.