{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T10:57:30Z","timestamp":1649069850756},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1996,6]]},"abstract":"<jats:p> Using simple counting arguments, the Feferman-Vaught techniques and selected results from universal algebra, we show that for any directly representable variety V there is a positive integer k such that for any first-order sentence \u03d5 the proportion of members of V of size at most x which satisfy \u03d5 tends to a limit belonging to [Formula: see text] as x goes to infinity. Furthermore there is a first-order statement for which the limit is [Formula: see text]. V has a 0\u20131 law (i.e., k=1) iff the finite members factor uniquely into directly indecomposables. <\/jats:p>","DOI":"10.1142\/s0218196796000131","type":"journal-article","created":{"date-parts":[[2004,10,25]],"date-time":"2004-10-25T12:13:15Z","timestamp":1098706395000},"page":"269-276","source":"Crossref","is-referenced-by-count":3,"title":["A DIRECTLY REPRESENTABLE VARIETY HAS A DISCRETE FIRST-ORDER LAW"],"prefix":"10.1142","volume":"06","author":[{"given":"STANLEY","family":"BURRIS","sequence":"first","affiliation":[{"name":"Dept. of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PAWEL","family":"IDZIAK","sequence":"additional","affiliation":[{"name":"Dept. of Computer Science, Jagiellonian University, Cracow, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196796000131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:00:08Z","timestamp":1565128808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196796000131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1996,6]]}},"alternative-id":["10.1142\/S0218196796000131"],"URL":"https:\/\/doi.org\/10.1142\/s0218196796000131","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6]]}}}