{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T07:50:12Z","timestamp":1773820212404,"version":"3.50.1"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":5068,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2000,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We propose an original use of techniques from random graph theory to find a Monadic<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1079898600006715_inline1\"\/>(Minimal Scott without equality) sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1079898600006715_inline1\"\/>(FO<jats:sup>2<\/jats:sup>) and]<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1079898600006715_inline1\"\/>(Minimal G\u00f6del without equality). Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the corresponding<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1079898600006715_inline1\"\/>fragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.<\/jats:p>","DOI":"10.2307\/421076","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T07:13:33Z","timestamp":1146986013000},"page":"67-82","source":"Crossref","is-referenced-by-count":15,"title":["Counterexamples of the 0-1 Law for Fragments of Existential Second-Order Logic: an Overview"],"prefix":"10.1017","volume":"6","author":[{"given":"Jean-Marie Le","family":"Bars","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600006715_ref021","unstructured":"Bars J-M. 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