{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:21:23Z","timestamp":1759335683530},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,8]]},"abstract":"<jats:p> We say that a finite algebra \ud835\udd38 = \u3008A; F\u3009 has the ability to count if there are subalgebras C of \ud835\udd38<jats:sup>3<\/jats:sup> and Z of \ud835\udd38 such that the structure \u3008A; C, Z\u3009 has the ability to count in the sense of Feder and Vardi. We show that for a core relational structure A the following conditions are equivalent: (i) the variety generated by the algebra \ud835\udd38 associated to A contains an algebra with the ability to count; (ii) \ud835\udd38<jats:sup>2<\/jats:sup> has the ability to count; (iii) the variety generated by \ud835\udd38 admits the unary or affine type. As a consequence, for CSP's of finite signature, the bounded width conjectures stated in Feder\u2013Vardi [10], Larose\u2013Z\u00e1dori [17] and Bulatov [5] are identical. <\/jats:p>","DOI":"10.1142\/s021819670900524x","type":"journal-article","created":{"date-parts":[[2009,9,3]],"date-time":"2009-09-03T07:03:24Z","timestamp":1251961404000},"page":"647-668","source":"Crossref","is-referenced-by-count":10,"title":["OMITTING TYPES, BOUNDED WIDTH AND THE ABILITY TO COUNT"],"prefix":"10.1142","volume":"19","author":[{"given":"BENOIT","family":"LAROSE","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve West, Montr\u00e9al, Qc, Canada, H3G 1M8, Canada"}]},{"given":"MATT","family":"VALERIOTE","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, McMaster University, 1280 Main Street, West Hamilton, Ontario, Canada L8S 4K1, Canada"}]},{"given":"L\u00c1SZL\u00d3","family":"Z\u00c1DORI","sequence":"additional","affiliation":[{"name":"Bolyai Int\u00e9zet, Aradi v\u00e9rtan\u00fak tere 1, H-6720, Szeged, Hungary"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90219-J"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-92800-3_5"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-92800-3_4"},{"key":"rf8","volume":"1","author":"Dalmau V.","journal-title":"Logical Methods in Computer Science"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539794266766"},{"key":"rf11","series-title":"London Mathematical Society Lecture Note Series","volume-title":"Commutator Theory for Congruence Modular Varieties","volume":"125","author":"Freese R.","year":"1987"},{"key":"rf12","author":"Hobby D.","journal-title":"Contemp. Math."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1995.1055"},{"key":"rf15","volume":"3","author":"Larose B.","journal-title":"Logical Methods in Computer Science"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.12.048"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-007-2012-6"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07003-1"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01157687"},{"key":"rf20","unstructured":"\u00c1.\u00a0Szendrei, Research and Exposition in Mathematics (Heldermann Verlag, 1992)\u00a0pp. 209\u2013239."},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700029979"},{"key":"rf22","volume-title":"Seminaires de Mathematiques Superieures","volume":"99","author":"Szendrei \u00c1.","year":"1986"},{"key":"rf23","first-page":"18","author":"Valeriote M.","journal-title":"Canadian J. Math."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819670900524X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:19:04Z","timestamp":1565115544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819670900524X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8]]},"references-count":17,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,8]]}},"alternative-id":["10.1142\/S021819670900524X"],"URL":"https:\/\/doi.org\/10.1142\/s021819670900524x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8]]}}}