{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T09:50:30Z","timestamp":1717840230271},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2002,11]]},"abstract":"<jats:p> In this paper, we investigate the Lindenbaum algebra \u2112(T<jats:sub> fin <\/jats:sub>) of the theory T<jats:sub> fin <\/jats:sub>= Th (M<jats:sub> fin <\/jats:sub>) of the class M<jats:sub> fin <\/jats:sub> of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its G\u00f6del numeration \u03b3 is a [Formula: see text]-numeration. Moreover, the quotient algebra (\u2112(T<jats:sub> fin <\/jats:sub>)\/\u2131, \u03b3\/\u2131) modulo the Fr\u00e9chet ideal \u2131 is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These conditions characterize uniquely the algebra \u2112(T<jats:sub> fin <\/jats:sub>); moreover, these conditions characterize up to recursive isomorphism the numerated Boolean quotient algebra (\u2112(T<jats:sub> fin <\/jats:sub>)\/\u2131, \u03b3\/\u2131). <\/jats:p><jats:p> These results extend the work of Trakhtenbrot [17] and Vaught [18] on the first order theory of the class of all finite models of a finite rich signature. <\/jats:p>","DOI":"10.1142\/s0219061302000163","type":"journal-article","created":{"date-parts":[[2002,11,19]],"date-time":"2002-11-19T05:30:53Z","timestamp":1037683853000},"page":"145-225","source":"Crossref","is-referenced-by-count":5,"title":["THE LINDENBAUM ALGEBRA OF THE THEORY OF THE CLASS OF ALL FINITE MODELS"],"prefix":"10.1142","volume":"02","author":[{"given":"STEFFEN","family":"LEMPP","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Wisconsin,  Madison, WI 53706-1388, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MIKHAIL","family":"PERETYAT'KIN","sequence":"additional","affiliation":[{"name":"Kazakh Academy of Sciences, Institute of Mathematics,  Alma-Ata 480100, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"REED","family":"SOLOMON","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Wisconsin,  Madison, WI 53706-1388, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00967504"},{"key":"p_5","first-page":"132","author":"Hanf W.","year":"1965","journal-title":"Amsterdam"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1975-13747-5"},{"key":"p_9","first-page":"140","volume":"30","author":"Odintsov C. P.","year":"1989","journal-title":"Siberian Math. J."},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02219840"},{"key":"p_14","first-page":"127","volume":"20","author":"Selivanov V. L.","year":"1991","journal-title":"Barnaul"},{"key":"p_17","first-page":"569","volume":"70","author":"Trakhtenbrot B. A.","year":"1950","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.2307\/2964336"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061302000163","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:32:06Z","timestamp":1565080326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061302000163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,11]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2002,11]]}},"alternative-id":["10.1142\/S0219061302000163"],"URL":"https:\/\/doi.org\/10.1142\/s0219061302000163","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,11]]}}}