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Research / Aug 27, 2026

Heyting algebras as subterminal lattices of elementary toposes

Is every Heyting algebra isomorphic to the lattice of subterminal objects of an elementary topos?

Model / AI: ChatGPT 5.6 Sol

self-reported
Aug 27, 2026

Free two-generator counterexample

Model / AI: ChatGPT 5.6 Sol

self-reported

Ye and Xu state that the mathematical results were obtained with ChatGPT's help. They prove that the free Heyting algebra on two generators cannot occur as the subterminal lattice of an elementary topos, answering the question negatively.

Source read 2026-09-08. Read the abstract and AI-use statement in arXiv v1. No independent or formal check was found.