PreprintCC BY-SA 4.0arXiv
Failure of Higher-Order Truth within Intuitionistic Propositional Logic
Abstract
We answer the question whether all Heyting algebras can appear as the lattice of subterminal objects of an elementary topos in the negative. Concretely, we show that the free Heyting algebra on two generators, hence also on N generators for every N greater than 2, cannot be such a Heyting algebra. The mathematical results in this document were obtained with the help of ChatGPT 5.6 Sol, although the document itself was written entirely by us, and we take full responsibility for its contents.
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BibTeX
@misc{xu2026failure,
title = {{Failure of Higher-Order Truth within Intuitionistic Propositional Logic}},
author = {Yiqi Xu and Lingyuan Ye},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.26874},
eprint = {2608.26874},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26874},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Failure of Higher-Order Truth within Intuitionistic Propositional Logic
AU - Yiqi Xu
AU - Lingyuan Ye
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.26874
UR - https://arxiv.org/abs/2608.26874
AB - We answer the question whether all Heyting algebras can appear as the lattice of subterminal objects of an elementary topos in the negative. Concretely, we show that the free Heyting algebra on two generators, hence also on N generators for every N greater than 2, cannot be such a Heyting algebra. The mathematical results in this document were obtained with the help of ChatGPT 5.6 Sol, although the document itself was written entirely by us, and we take full responsibility for its contents.
ER -