直觉主义命题逻辑中的高阶真值失效
Failure of Higher-Order Truth within Intuitionistic Propositional Logic
AI总结：
本文否定回答了所有Heyting代数能否作为初等拓扑斯的次终端对象格出现的问题，证明了两生成元的自由Heyting代数无法成为该类Heyting代数，相关结果借助ChatGPT 5.6 Sol获得。
AI中文摘要：
我们否定回答了所有Heyting代数能否作为初等拓扑斯的次终端对象格出现的问题，具体证明了由两个生成元生成的自由Heyting代数无法成为这样的Heyting代数。本文的数学结果借助ChatGPT 5.6 Sol获得，文档本身完全由我们撰写，我们对内容负全部责任。
英文摘要：
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.
