On hereditarily small sets in ZF |
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| Authors: | M Randall Holmes |
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| Institution: | Department of Mathematics, Boise State University, 1910 University Drive, , Boise, ID, 83725 United States of America |
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| Abstract: | We show in  (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  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  (where the collection under consideration is the set of hereditarily countable sets). |
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