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arXiv:2206.08283 [math.LO]AbstractReferencesReviewsResources

Constructing the Constructible Universe Constructively

Richard Matthews, Michael Rathjen

Published 2022-06-16Version 1

We study the properties of the constructible universe, L, over intuitionistic theories. We give an extended set of fundamental operations which is sufficient to generate the universe over Intuitionistic Kripke-Platek set theory without Infinity. Following this, we investigate when L can fail to be an inner model in the traditional sense. Namely, we first show that, over Intuitionistic Zermelo-Fraenkel, it is possible for there to be an ordinal which is not in the constructible universe. Then we show that Constructive Zermelo-Fraenkel (even with the Power Set axiom) cannot prove that the Axiom of Exponentiation holds in L.

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