{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T17:22:08Z","timestamp":1649092928561},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8320,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:p>In [9] and [10] P. Kolaitis and M. Vardi proved that the 0-1 law holds for the second-order existential sentences whose first-order parts are formulas of Bernays-Schonfinkel or Ackermann prefix classes. They also provided several examples of second-order formulas for which the 0-1 law does not hold, and noticed that the classification of second-order sentences for which the 0-1 law holds resembles the classification of decidable cases of first-order prenex sentences. The only cases they have not settled are the cases of G\u00f6del classes with and without equality.<\/jats:p><jats:p>In this paper we confirm the conjecture of Kolaitis and Vardi that the 0-1 law does not hold for the existential second-order sentences whose first-order part is in G\u00f6del prenex form with equality. The proof we give is based on a modification of the example employed by W. Goldfarb [5] in his proof that, contrary to the G\u00f6del claim [6], the class of G\u00f6del prenex formulas with equality is undecidable.<\/jats:p>","DOI":"10.2307\/2274691","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:39:41Z","timestamp":1146940781000},"page":"427-438","source":"Crossref","is-referenced-by-count":3,"title":["Asymptotic probabilities of existential second-order G\u00f6del sentences"],"prefix":"10.1017","volume":"56","author":[{"given":"Leszek","family":"Pacholski","sequence":"first","affiliation":[]},{"given":"Wies\u0141aw","family":"Szwast","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200024464_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(85)80027-9"},{"key":"S0022481200024464_ref007","volume-title":"A counterexample to the 0-1 law for existential monadic second-order logic","author":"Kaufmann","year":"1987"},{"key":"S0022481200024464_ref003","first-page":"50","volume":"41","author":"Fagin","year":"1976","journal-title":"Probabilities on finite models"},{"key":"S0022481200024464_ref011","first-page":"156","volume-title":"Proceedings of the 5th Annual Symposium on Logic in Computer Science","author":"Kolaitis","year":"1990"},{"key":"S0022481200024464_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(85)90112-8"},{"key":"S0022481200024464_ref013","first-page":"279","article-title":"Enumerable sets are Diophantine","volume":"191","author":"Matijasevi\u010d","year":"1970","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S0022481200024464_ref002","volume-title":"The decision problem: solvable classes of quantificational formulas","author":"Dreben","year":"1979"},{"key":"S0022481200024464_ref006","first-page":"27","article-title":"Ein Spezialfall des Entscheidungsproblems der theoretischien Logik","volume":"2","author":"G\u00f6del","year":"1932","journal-title":"Ergebnisse eines Mathematischen Kolloquiums"},{"key":"S0022481200024464_ref009","first-page":"425","volume-title":"Proceedings of the 19th ACM Symposium on Theory on Computing","author":"Kolaitis","year":"1987"},{"key":"S0022481200024464_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01071084"},{"key":"S0022481200024464_ref010","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1109\/LICS.1988.5095","volume-title":"Proceedings of the 3rd Annual Symposium on Logic in Computer Science","author":"Kolaitis","year":"1988"},{"key":"S0022481200024464_ref012","volume-title":"Unsolvable classes of quantificational formulas","author":"Lewis","year":"1979"},{"key":"S0022481200024464_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1984-15207-8"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200024464","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,17]],"date-time":"2019-05-17T17:45:59Z","timestamp":1558115159000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200024464\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["S0022481200024464"],"URL":"https:\/\/doi.org\/10.2307\/2274691","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}