{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:22:59Z","timestamp":1759335779884},"reference-count":24,"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":[[2006,6]]},"abstract":"<jats:p> A lattice L is coordinatizable, if it is isomorphic to the lattice L(R) of principal right ideals of some von Neumann regular ring R. This forces L to be complemented modular. All known sufficient conditions for coordinatizability, due first to von Neumann, then to J\u00f3nsson, are first-order. Nevertheless, we prove that coordinatizability of lattices is not first-order, by finding a non-coordinatizable lattice K with a coordinatizable countable elementary extension L. This solves a 1960 problem of J\u00f3nsson. We also prove that there is no [Formula: see text] statement equivalent to coordinatizability. Furthermore, the class of coordinatizable lattices is not closed under countable directed unions; this solves another problem of J\u00f3nsson from 1962. <\/jats:p>","DOI":"10.1142\/s0219061306000499","type":"journal-article","created":{"date-parts":[[2006,7,24]],"date-time":"2006-07-24T09:26:26Z","timestamp":1153733186000},"page":"1-24","source":"Crossref","is-referenced-by-count":8,"title":["VON NEUMANN COORDINATIZATION IS NOT FIRST-ORDER"],"prefix":"10.1142","volume":"06","author":[{"given":"FRIEDRICH","family":"WEHRUNG","sequence":"first","affiliation":[{"name":"LMNO, CNRS UMR 6139, Universit\u00e9 de Caen, Campus II, D\u00e9partement de Math\u00e9matiques, B.P. 5186, 14032 CAEN Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","series-title":"Cahiers Scientifiques, Fascicule","volume-title":"Alg\u00e8bre G\u00e9om\u00e9trique","volume":"27","author":"Artin E.","year":"1978"},{"key":"rf2","unstructured":"M. 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