Year: 2025
Type: article
Abstract: A poset $${\mathbb {X}}$$ X is said to be zigzag image-finite, if the least updownset (i.e., both an upset and a downset) containing x is finite, for all $$x\in X.$$ x ∈ X . We show that a bi-Heyting algebra is profinite if and only if it is isomorphic to the lattice of upsets of a zigzag image-finite poset. Zigzag image-finite posets have the property of being disjoint unions of finite connected posets. Because of this, we equivalently show that a bi-Heyting algebra is profinite if and only if it is isomorphic to a direct product of simple finite bi-Heyting algebras.
Source: Algebra Universalis
Author: Lydia Tasiou
Institution: University of Amsterdam
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4410217825