@inproceedings{f91a01c09b6c49f6b87b47e57763a362,
title = "First-Order Logic with Equicardinality in Random Graphs",
abstract = "We answer a question of Blass and Harary about the validity of the zero-one law in random graphs for extensions of first-order logic (FOL). For a given graph property P, the Lindstr{\"o}m extension of FOL by P is defined as the minimal (regular) extension of FOL able to express P. For several graph properties P (e.g. Hamiltonicity), it is known that the Lindstr{\"o}m extension by P is also able to interpret a segment of arithmetic, and thus strongly disobeys the zero-one law. Common to all these properties is the ability to express the H{\"a}rtig quantifier, a natural extension of FOL testing if two definable sets are of the same size. We prove that the H{\"a}rtig quantifier is sufficient for the interpretation of arithmetic, thus providing a general result which implies all known cases of Lindstr{\"o}m extensions which are able to interpret a segment of arithmetic.",
keywords = "equicardinality, finite model theory, first-order logic, generalized quantifiers, monadic second-order logic, random graphs, zero-one laws",
author = "Simi Haber and Tal Hershko and Mostafa Mirabi and Saharon Shelah",
note = "Publisher Copyright: {\textcopyright} Simi Haber, Tal Hershko, Mostafa Mirabi, and Saharon Shelah.; 33rd EACSL Annual Conference on Computer Science Logic, CSL 2025 ; Conference date: 10-02-2025 Through 14-02-2025",
year = "2025",
month = feb,
day = "3",
doi = "10.4230/LIPIcs.CSL.2025.12",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Jorg Endrullis and Sylvain Schmitz",
booktitle = "33rd EACSL Annual Conference on Computer Science Logic, CSL 2025",
address = "ألمانيا",
}