{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T11:19:32Z","timestamp":1772450372954,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p> We introduce the notion of a preindependence relation between subsets of the big model of a complete first-order theory, an abstraction of the properties which numerous concrete notions such as forking, dividing, thorn-forking, thorn-dividing, splitting or finite satisfiability share in all complete theories. We examine the relation between four additional axioms (extension, local character, full existence and symmetry) that one expects of a good notion of independence. <\/jats:p><jats:p> We show that thorn-forking can be described in terms of local forking if we localize the number k in Kim's notion of \"dividing with respect to k\" (using Ben-Yaacov's \"k-inconsistency witnesses\") rather than the forking formulas. It follows that every theory with an M-symmetric lattice of algebraically closed sets (in T<jats:sup>eq<\/jats:sup>) is rosy, with a simple lattice theoretical interpretation of thorn-forking. <\/jats:p>","DOI":"10.1142\/s0219061309000823","type":"journal-article","created":{"date-parts":[[2010,7,15]],"date-time":"2010-07-15T04:16:53Z","timestamp":1279167413000},"page":"21-38","source":"Crossref","is-referenced-by-count":9,"title":["THORN-FORKING AS LOCAL FORKING"],"prefix":"10.1142","volume":"09","author":[{"given":"HANS","family":"ADLER","sequence":"first","affiliation":[{"name":"Kurt G\u00f6del Research Center for Mathematical Logic, W\u00e4hringer Str. 25, 1090 Wien, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061309000811"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665578"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-46248-1"},{"key":"rf5","volume-title":"Complemented Modular Lattices and Regular Rings","author":"Skornyakov L. A.","year":"1964"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310051"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610798005985"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061303000297"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.4064\/fm179-3-2"},{"key":"rf10","volume-title":"Classification Theory and the Number of Non-Isomorphic Models","author":"Shelah S.","year":"1978"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00050-5"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1140641160"},{"key":"rf14","first-page":"368","volume":"29","author":"Evans D. M.","journal-title":"Algebra Log."}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061309000823","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:29:44Z","timestamp":1565137784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061309000823"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":12,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2009,6]]}},"alternative-id":["10.1142\/S0219061309000823"],"URL":"https:\/\/doi.org\/10.1142\/s0219061309000823","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}