A Naive Encoding of Russell's Paradox in Type Theory
Logic
2026-01-06 v1 Logic in Computer Science
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).
Cite
@article{arxiv.2601.00811,
title = {A Naive Encoding of Russell's Paradox in Type Theory},
author = {Zhuoyuan Qu},
journal= {arXiv preprint arXiv:2601.00811},
year = {2026}
}