A class of higher inductive types in Zermelo‐Fraenkel set theory

Mathematical Logic Quarterly 68 (1):118-127 (2022)
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Abstract

We define a class of higher inductive types that can be constructed in the category of sets under the assumptions of Zermelo‐Fraenkel set theory without the axiom of choice or the existence of uncountable regular cardinals. This class includes the example of unordered trees of any arity.

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10.1002/malq.202100040

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Wellfounded trees in categories.Ieke Moerdijk & Erik Palmgren - 2000 - Annals of Pure and Applied Logic 104 (1-3):189-218.
On hereditarily countable sets.Thomas Jech - 1982 - Journal of Symbolic Logic 47 (1):43-47.
On hereditarily small sets in ZF.M. Randall Holmes - 2014 - Mathematical Logic Quarterly 60 (3):228-229.

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