A Lindström theorem for intuitionistic first-order logic

2021/03/31 by Grigory K. Olkhovikov, Olkhovikov, Grigory, Guillermo Badía +3
Computer Science · Economics, Econometrics and Finance · #03B20 #03B55 #03C95 #Advanced Algebra and Logic #FOS: Mathematics #Game Theory and Voting Systems #Logic (math.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.2103.17024

openalex publication_date 2021/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the main result of (G. Badia and G. Olkhovikov. A Lindström theorem for intuitionistic propositional logic. Notre Dame Journal of Formal Logic, 61 (1): 11--30 (2020)) to the first-order intuitionistic logic (with and without equality), showing that it is the maximal (with respect to expressive power) abstract logic satisfying a certain form of compactness, the Tarski union property and preservation under asimulations. A similar result is also shown for the intuitionistic logic of constant domains.

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• Maximality of bi-intuitionistic propositional logic
• Maximality of logic without identity
• The Lindstrom's Characterizability of Abstract Logic Systems for Analytic Structures Based on Measures
• Mathematical semantics of intuitionistic logic
• A complete axiomatization of infinitary first-order intuitionistic logic over L_{κ⁺, κ}