Year: 2026
Type: preprint
Abstract: We present two new applications of Simmons' point-free Cantor-Bendixson coderivative operator in intuitionistic logic. First, we use it to give a simplified proof of the recent result of Xu and Ye that the free Heyting algebra on two generators does not occur as the Heyting algebra of subterminal objects in any elementary topos. Then we use it to prove that complete Heyting algebra semantics is not strongly complete for intuitionistic second-order propositional logic: semantic consequence from an arbitrary set of assumptions does not coincide with ordinary syntactic consequence.
Source: arXiv (Cornell University)
Author: Kocsis, Zoltan A.
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214315205