On hereditarily small sets in ZF

Mathematical Logic Quarterly 60 (3):228-229 (2014)
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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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10.1002/malq.201300089

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Citations of this work

A class of higher inductive types in Zermelo‐Fraenkel set theory.Andrew W. Swan - 2022 - Mathematical Logic Quarterly 68 (1):118-127.

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On hereditarily countable sets.Thomas Jech - 1982 - Journal of Symbolic Logic 47 (1):43-47.

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