Preservation under Reduced Products in Continuous Logic

2024/05/21 by Ivory Fronteau, Fronteau, Ivory
Computer Science · #Advanced Database Systems and Queries #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.2405.12720

openalex publication_date 2024/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a fragment of continuous first-order logic, analogue of Palyutin formulas (or h-formulas) in classical model theory, which is preserved under reduced products in both directions. We use it to extend classical results on complete theories which are preserved under reduced product and their stability. We also characterize the set of Palyutin sentences, Palyutin theories and other related fragments in terms of their preservation properties, both in the classical setting and the metric one.

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