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The research investigates uniform local tabularity in intuitionistic logic, focusing on its algebraic structures.

July 1, 2026Open Access

Uniform Local Tabularity in Intuitionistic Logic

Key Points

The research investigates uniform local tabularity in intuitionistic logic, focusing on its algebraic structures.
Analyzed the implications of uniform local tabularity in relation to Heyting algebras.
Provided an axiomatization for n-uniform locally finite Heyting algebras for n ≤ 3.
Presented examples of logics that are not uniformly locally tabular.
Demonstrated that n-uniformly locally finite Heyting algebras consistently form a variety.
Established a direct comparison between locally finite and n-uniformly locally finite Heyting algebras.
Provided an explicit example of a pre-uniformly locally tabular logic, clarifying Shehtman's earlier question.

Abstract

By contrast with S4, the analysis of local tabularity above IPC has provided a difficult challenge.This paper studies a strengthening of local tabularity -uniform local tabularity -where one demands that all formulas be equivalent to formulas of a given implication depth.Algebraically, this amounts to considering Heyting algebras generated by finitely many iterations of the implication operation.It is shown that in contrast with locally finite Heyting algebras, n-uniformly locally finite Heyting algebras always form a variety, and an explicit axiomatization of the variety of n-uniform locally finite Heyting algebras for n ≤ 3 is given.In connection with this analysis, it is shown that there exist locally tabular logics which are not uniformly locally tabular, answering a question of Shehtman -an example of a pre-uniformly locally tabular logic is presented, which is shown to be the unique pre-uniformly locally tabular extension of the system KG.

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