{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T16:26:42Z","timestamp":1776702402255,"version":"3.51.2"},"reference-count":15,"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> A ternary relation [Formula: see text] between subsets of the big model of a complete first-order theory T is called an independence relation if it satisfies a certain set of axioms. The primary example is forking in a simple theory, but o-minimal theories are also known to have an interesting independence relation. Our approach in this paper is to treat independence relations as mathematical objects worth studying. The main application is a better understanding of thorn-forking, which turns out to be closely related to modular pairs in the lattice of algebraically closed sets. <\/jats:p>","DOI":"10.1142\/s0219061309000811","type":"journal-article","created":{"date-parts":[[2010,7,15]],"date-time":"2010-07-15T08:16:53Z","timestamp":1279181813000},"page":"1-20","source":"Crossref","is-referenced-by-count":48,"title":["A GEOMETRIC INTRODUCTION TO FORKING AND THORN-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","volume-title":"Classification Theory and the Number of Non-Isomorphic Models","author":"Shelah S.","year":"1978"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610798005985"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1986-0833697-X"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1140641160"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1191333848"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061309000823"},{"key":"rf9","first-page":"368","volume":"29","author":"Evans D. M.","journal-title":"Algebra Log."},{"key":"rf11","first-page":"311","volume":"59","author":"Lee F. L.","journal-title":"J. Symb. Log."},{"key":"rf12","volume-title":"Continuous Geometry","author":"von Neumann J.","year":"1960"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(97)00019-5"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061303000297"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(80)90009-1"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00066-6"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.2307\/1968934"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.2307\/2695047"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061309000811","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T04:29:42Z","timestamp":1565152182000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061309000811"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":15,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2009,6]]}},"alternative-id":["10.1142\/S0219061309000811"],"URL":"https:\/\/doi.org\/10.1142\/s0219061309000811","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}