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Ehrenfeucht-Fraïssé Games for Continuous First-Order Logic

2024/02/26 by Åsa Hirvonen, Hirvonen, Åsa, Joni Puljujärvi +1
Computer Science · #03C66 #03C75 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2402.16662

openalex publication_date 2024/02/26 · openalex created_date 2024/02/28 · openalex updated_date 2026/08/04

Abstract

We define a version of the Ehrenfeucht-Fraïssé game in the setting of metric model theory and continuous first-order logic and show that the second player having a winning strategy in a game of length n exactly corresponds to being elementarily equivalent up to quantifier rank n. We then demonstrate the usefulness of the game with some examples. Finally, we discus connections between the game of length ω and infinitary logic.

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