Goldblatt-Thomason Theorems for Inflationary Intuitionistic Logic

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发表日期：

2025年10月4日

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Minghui Ma

摘要

Inflationary intuitionistic logic is the extension of intuitionistic logic with an inflationary operator. Algebraic and relational semantics for inflationary intuitionistic logic are developed. Goldblatt-Thomason theorems are proved by a representation theory for inflationary Heyting algebras and inflationary modal frames. Some characterization theorems for the definability of special frame classes are further proved. The method of Jankov-formulas is utilized to prove a Goldblatt-Thomason theorem for finite frames. The connections between transit definability and $\textsf{K4}$ $K 4$ -frame definability are established by a splitting translation of Esakia’s modalized Heyting calculus $\textsf{mHC}$ $mHC$ into the modal logic $\textsf{K4}$ $K 4$ .