@inproceedings{10.1145/3531130.3532498,
    Abstract = {This paper investigates the expressiveness of a fragment of first-order 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 \L{}\'{o}s-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.},
    Address = {New York, NY, USA},
    Author = {Lopez, Aliaume},
    BookTitle = {Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science},
    File = {When Locality Meets Preservation - 3531130.3532498.pdf},
    ISBN = {9781450393515},
    Keywords = {Well quasi ordering, Gaifman normal form, Locality, Undecidability, Preservation theorem, Tree depth, Finite Model Theory.},
    Location = {Haifa, Israel},
    Publisher = {Association for Computing Machinery},
    Series = {LICS '22},
    Title = {When Locality Meets Preservation},
    URL = {https://doi.org/10.1145/3531130.3532498},
    Year = {2022},
    articleno = {46},
    bdsk-url-1 = {https://doi.org/10.1145/3531130.3532498},
    date-added = {2022-08-29 14:27:27 +0200},
    date-modified = {2022-08-29 14:27:27 +0200},
    numpages = {14},
    doi = {10.1145/3531130.3532498}
}

@inproceedings{10.1145/3531130.3532498, Abstract = {This paper investigates the expressiveness of a fragment of first-order 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 \L{}\'{o}s-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.}, Address = {New York, NY, USA}, Author = {Lopez, Aliaume}, BookTitle = {Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science}, File = {When Locality Meets Preservation - 3531130.3532498.pdf}, ISBN = {9781450393515}, Keywords = {Well quasi ordering, Gaifman normal form, Locality, Undecidability, Preservation theorem, Tree depth, Finite Model Theory.}, Location = {Haifa, Israel}, Publisher = {Association for Computing Machinery}, Series = {LICS '22}, Title = {When Locality Meets Preservation}, URL = {https://doi.org/10.1145/3531130.3532498}, Year = {2022}, articleno = {46}, bdsk-url-1 = {https://doi.org/10.1145/3531130.3532498}, date-added = {2022-08-29 14:27:27 +0200}, date-modified = {2022-08-29 14:27:27 +0200}, numpages = {14}, doi = {10.1145/3531130.3532498} }