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Logic"],"published-print":{"date-parts":[[2024,4,30]]},"abstract":"<jats:p>\n            The\n            <jats:italic>k<\/jats:italic>\n            -spectrum is the set of all\n            <jats:italic>\u03b1<\/jats:italic>\n            &gt; 0 such that\n            <jats:italic>G(n,n<\/jats:italic>\n            <jats:sup>\u2212\u03b1<\/jats:sup>\n            ) does not obey the 0-1 law for FO sentences with quantifier depth at most\n            <jats:italic>k<\/jats:italic>\n            . In this article, we prove that the minimum\n            <jats:italic>k<\/jats:italic>\n            such that the\n            <jats:italic>k<\/jats:italic>\n            -spectrum is infinite equals 5.\n          <\/jats:p>","DOI":"10.1145\/3641547","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T11:53:17Z","timestamp":1705924397000},"page":"1-24","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Spectrum of FO Logic with Quantifier Depth 4 is Finite"],"prefix":"10.1145","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-2418-8206","authenticated-orcid":false,"given":"Yury","family":"Yarovikov","sequence":"first","affiliation":[{"name":"Moscow Institute of Physics and Technology, Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8763-9533","authenticated-orcid":false,"given":"Maksim","family":"Zhukovskii","sequence":"additional","affiliation":[{"name":"The University of Sheffield, Sheffield, United Kingdom"}]}],"member":"320","published-online":{"date-parts":[[2024,3,28]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/9780470277331"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579198"},{"issue":"129","key":"e_1_3_1_4_2","first-page":"13","article-title":"An application of games to the completeness problem for formalized theories","volume":"49","author":"Ehrenfeucht Andrzej","year":"1961","unstructured":"Andrzej Ehrenfeucht. 1961. 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