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arXiv · 2601.00811

A Naive Encoding of Russell's Paradox in Type Theory

Zhuoyuan Qu
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Abstract

Russell's paradox is the most easily understandable way to illustrate the inconsistency of na\"ive set theory. This note proposes a direct encoding of Russell's paradox with type-in-type universe, sigma types, and either extensional identity or intensional identity with the uniqueness of identity proofs (UIP).

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Zhuoyuan Qu. 2025-12-22. A Naive Encoding of Russell's Paradox in Type Theory. https://arxiv.org/abs/2601.00811

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