{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T09:35:14Z","timestamp":1648892114333},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4210,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In [9] we introduced a new framework for asymptotic probabilities, in which a \u03c3-additive measure is defined on the sample space of all sequences <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009440_inline1\" \/> of finite models, where the universe of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009440_inline2\" \/>, is {1,2,\u2026,<jats:italic>n<\/jats:italic>}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009440_inline2\" \/> eventually almost surely or fails in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009440_inline2\" \/> eventually almost surely.<\/jats:p><jats:p>In this paper we define the strong convergence law for formulas, which carries over the ideas of the strong 0-1 law to formulas with free variables, and roughly states that for each formula <jats:italic>\u03d5<\/jats:italic>(<jats:italic>x<\/jats:italic>), the fraction of tuples <jats:bold><jats:italic>a<\/jats:italic><\/jats:bold> in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009440_inline2\" \/>, which satisfy the formula <jats:italic>\u03d5<\/jats:italic>(<jats:italic>x<\/jats:italic>), almost surely has a limit as <jats:italic>n<\/jats:italic> tends to infinity.<\/jats:p><jats:p>We show that the infinitary logic with finitely many variables has the strong convergence law for formulas for the uniform measure, and further characterize the measures on random graphs for which the strong convergence law holds.<\/jats:p>","DOI":"10.2178\/jsl\/1190150151","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:14:26Z","timestamp":1197573266000},"page":"1083-1092","source":"Crossref","is-referenced-by-count":0,"title":["Strong convergence in finite model theory"],"prefix":"10.1017","volume":"67","author":[{"given":"Wafik Boulos","family":"Lotfallah","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009440_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1988-0924703-8"},{"key":"S0022481200009440_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1991-1102581-4"},{"key":"S0022481200009440_ref012","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511813658"},{"key":"S0022481200009440_ref001","first-page":"353","volume-title":"NATO Advanced Study Institute on Algorithms and Order","author":"Compton","year":"1987"},{"key":"S0022481200009440_ref007","first-page":"110","volume-title":"Kibernetika","author":"Knyazev","year":"1990"},{"key":"S0022481200009440_ref009","first-page":"1686","volume":"65","author":"Lotfallah","year":"2000","journal-title":"Strong 0-1 laws in finite model theory"},{"key":"S0022481200009440_ref002","first-page":"17","volume":"41","author":"Fagin","year":"1976","journal-title":"Probabilities on finite models"},{"key":"S0022481200009440_ref006","volume-title":"Logic Symposium'76","author":"Keisler","year":"1977"},{"key":"S0022481200009440_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01071084"},{"key":"S0022481200009440_ref004","volume-title":"Measure Theory","author":"Halmos","year":"1974"},{"key":"S0022481200009440_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(92)90021-7"},{"key":"S0022481200009440_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/421173"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009440","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:45:06Z","timestamp":1557189906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009440\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["S0022481200009440"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150151","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}