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Journal Articles Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science Year : 2022

When Locality Meets Preservation

Localité et théorèmes de préservation en logique du premier ordre

Abstract

This paper investigates the expressiveness of a fragment of firstorder sentences in Gaifman normal form, namely the positive Boolean combinations of basic local sentences. We show that they match exactly the first-order sentences preserved under local elementary embeddings, thus providing a new general preservation theorem and extending the Łós-Tarski Theorem. This full preservation result fails as usual in the finite, and we show furthermore that the naturally related decision problems are undecidable. In the more restricted case of preservation under extensions, it nevertheless yields new well-behaved classes of finite structures: we show that preservation under extensions holds if and only if it holds locally.
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Dates and versions

hal-03883990 , version 1 (04-12-2022)

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Attribution - NonCommercial - ShareAlike

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Aliaume Lopez. When Locality Meets Preservation. Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science, 2022, pp.1-14. ⟨10.1145/3531130.3532498⟩. ⟨hal-03883990⟩
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