{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:26Z","timestamp":1753894406534,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,1,29]]},"abstract":"<jats:p>We study multi-structural games, played on two sets $\\mathcal{A}$ and $\\mathcal{B}$ of structures. These games generalize Ehrenfeucht-Fra\\&amp;quot;{i}ss\\'{e} games. Whereas Ehrenfeucht-Fra\\&amp;quot;{i}ss\\'{e} games capture the quantifier rank of a first-order sentence, multi-structural games capture the number of quantifiers, in the sense that Spoiler wins the $r$-round game if and only if there is a first-order sentence $\\phi$ with at most $r$ quantifiers, where every structure in $\\mathcal{A}$ satisfies $\\phi$ and no structure in $\\mathcal{B}$ satisfies $\\phi$. We use these games to give a complete characterization of the number of quantifiers required to distinguish linear orders of different sizes, and develop machinery for analyzing structures beyond linear orders.<\/jats:p>","DOI":"10.46298\/lmcs-21(1:10)2025","type":"journal-article","created":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T11:15:09Z","timestamp":1738149309000},"source":"Crossref","is-referenced-by-count":0,"title":["Multi-Structural Games and Number of Quantifiers"],"prefix":"10.46298","volume":"Volume 21, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7374-0347","authenticated-orcid":false,"given":"Ronald","family":"Fagin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9427-8470","authenticated-orcid":false,"given":"Jonathan","family":"Lenchner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7382-7178","authenticated-orcid":false,"given":"Kenneth W.","family":"Regan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4055-7693","authenticated-orcid":false,"given":"Nikhil","family":"Vyas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2025,1,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/15161\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/15161\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T11:15:09Z","timestamp":1738149309000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/9181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(1:10)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2104.14709v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2104.14709v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2104.14709","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2104.14709","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,1,29]]},"article-number":"9181"}}