2021/11/26 by Vladimir Kanovei, Kanovei, Vladimir, Vassily Lyubetsky +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms
paper · pdf · doi:10.48550/arxiv.2111.13491
A set is nontypical in the Russell sense, if it belongs to a countable\nordinal definable set. The class HNT of all hereditarily nontypical sets\nsatisfies all axioms of ZF and the double inclusion HOD \⊆ HNT\n\⊆ V holds. Solving a problem recently proposed by Tzouvaras, a\ngeneric extension L[a,x] of L, by two reals a,x, is presented in which\nL=HOD subsetneqq L[a]=HNT subsetneqq V=L[a,x], so that HNT is a model\nof ZFC strictly between HOD and the universe.\n