{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:56:40Z","timestamp":1787507800557,"version":"build-2736575974"},"reference-count":17,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T00:00:00Z","timestamp":1289952000000},"content-version":"vor","delay-in-days":4338,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We show that the existential preservation theorem fails for two\u2010variable first\u2010order logic FO\n                    <jats:sup>2<\/jats:sup>\n                    . It is known that for all\n                    <jats:italic>k<\/jats:italic>\n                    \u2265 3, FO\n                    <jats:sup>k<\/jats:sup>\n                    does not have an existential preservation theorem, so this settles the last open case, answering a question of Andreka, van Benthem, and N\u00e9meti. In contrast, we prove that the homomorphism preservation theorem holds for FO\n                    <jats:sup>2<\/jats:sup>\n                    .\n                  <\/jats:p>","DOI":"10.1002\/malq.19990450304","type":"journal-article","created":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T11:30:38Z","timestamp":1289993438000},"page":"315-325","source":"Crossref","is-referenced-by-count":15,"title":["On Preservation Theorems for Two\u2010Variable Logic"],"prefix":"10.1002","volume":"45","author":[{"given":"Erich","family":"Gradel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric","family":"Rosen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2010,11,17]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-63246-8_2"},{"key":"e_1_2_1_3_2","unstructured":"Andreka H. J.van BENTHEM andI. Nemeti Modal languages and bounded fragments of predicate logic. ILLC Research Report ML\u201096\u201303 1996."},{"key":"e_1_2_1_4_2","volume-title":"Modal Logic and Classical Logic","author":"van BENTHEM J.","year":"1983"},{"key":"e_1_2_1_5_2","volume-title":"Model Theory","author":"Chang C. C","year":"1990"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1995.1084"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03182-7"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/421196"},{"key":"e_1_2_1_9_2","unstructured":"Gradel E. andM.Otto On logics with two variables. Theoret. Comput. Science (to appear)."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099486"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"e_1_2_1_12_2","first-page":"111","article-title":"Finite variable logics","volume":"51","author":"Hodkinson I.","year":"1993","journal-title":"Bulletin of the European Association for Theoretical Computer Science"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19750210118"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21676-7"},{"key":"e_1_2_1_15_2","unstructured":"Rosen E. Finite model theory and finite variable logic. PhD thesis University of Pennsylvania 1995."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008275906015"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-60178-3_99"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.2307\/2964569"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19990450304","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19990450304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T13:38:01Z","timestamp":1698586681000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19990450304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1002\/malq.19990450304"],"URL":"https:\/\/doi.org\/10.1002\/malq.19990450304","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}