2018/10/22 by Michał M. Stronkowski, Stronkowski, Michał M. · 1 citation
Computer Science · #03B45 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1810.09286
openalex publication_date 2018/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Blok-Esakia theorem states that there is an isomorphism from the lattice of intermediate logics onto the lattice of normal extensions of Grzegorczyk modal logic. The extension for multi-conclusion consequence relations was obtained by Emil Jeřábek as an application of canonical rules. We show that Jeřábek's result follows already from Blok's algebraic proof. We also prove that the properties of strong structural completeness and strong universal completeness are preserved and reflects by the aforementioned isomorphism. These properties coincide with structural completeness and universal completeness respectively for single-conclusion consequence relations and, in particular, for logics.