Abstract
We show in ZF (the usual set theory without Choice) that for any set X, the collection of sets Y such that each element of the transitive closure of {Y} is strictly smaller in size than X (the collection of sets hereditarily smaller than X) is a set. This result has been shown by Jech in the case X=ω1 (where the collection under consideration is the set of hereditarily countable sets).
Original language | English |
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Pages (from-to) | 228-229 |
Number of pages | 2 |
Journal | Mathematical Logic Quarterly |
Volume | 60 |
Issue number | 3 |
DOIs | |
State | Published - May 2014 |