On Elementary Theories of GLP-Algebras

2014/12/15 by Fedor Pakhomov, Pakhomov, Fedor
Computer Science · #03B25 #03F45 #Advanced Algebra and Logic #F.4.1 #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.1412.4439

openalex publication_date 2014/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There is a polymodal provability logic GLP. We consider generalizations of this logic: the logics GLP_α, where α ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the varieties of modal algebras that corresponds to the polymodal logics. We prove that the elementary theories of the free ∅-generated GLP_n -algebras are decidable for all finite ordinals n.

Citations

• Provability interpretations of modal logic

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