{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:01:52Z","timestamp":1760954512946},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2003,6]]},"abstract":"<jats:p>For various proper inclusions of classes of groups [Formula: see text], we obtain a group [Formula: see text] and a first-order sentence \u03c6 such that H\u22a8\u03c6 but no G\u2208 C satisfies \u03c6. The classes we consider include the finite, finitely presented, finitely generated with and without solvable word problem, and all countable groups. For one separation, we give an example of a f.g. group, namely \u2124<jats:sub>p<\/jats:sub>\u2240 \u2124 for some prime p, which is the only f.g. group satisfying an appropriate first-order sentence. A further example of such a group, the free step-2 nilpotent group of rank 2, is used to show that true arithmetic Th(\u2115,+,\u00d7) can be interpreted in the theory of the class of finitely presented groups and other classes of f.g. groups.<\/jats:p>","DOI":"10.1142\/s0218196703001286","type":"journal-article","created":{"date-parts":[[2003,8,20]],"date-time":"2003-08-20T09:30:13Z","timestamp":1061371813000},"page":"287-302","source":"Crossref","is-referenced-by-count":23,"title":["Separating Classes of Groups by First-Order Sentences"],"prefix":"10.1142","volume":"13","author":[{"given":"Andr\u00e9","family":"Nies","sequence":"first","affiliation":[{"name":"Department of Computer Science, The University of Auckland, Private Bag 92109, Auckland, New Zealand"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1994-1202419-X"},{"key":"rf2","first-page":"305","volume":"34","author":"Hall P.","journal-title":"J. London Math. Soc."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700018152"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0099387"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511551574"},{"key":"rf6","unstructured":"C. F.\u00a0Miller\u00a0III, Aspects of Effective Algebra, ed. J. N.\u00a0Crossley (Upside down a book company, 1981)\u00a0pp. 209\u2013210."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-9964-6"},{"key":"rf8","series-title":"Oxford Logic Guides","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198532132.001.0001","volume-title":"Models of Peano Arithmetic","volume":"15","author":"Kaye R.","year":"1991"},{"key":"rf9","first-page":"101","author":"Kharlampovich O.","journal-title":"Electronic Res. Announce. AMS"},{"key":"rf10","volume-title":"Algebra","author":"Lang S.","year":"1965"},{"key":"rf11","first-page":"221","volume":"45","author":"Mal'cev A.","journal-title":"Amer. Math. Soc. Trans."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190967"},{"key":"rf13","first-page":"293","volume":"30","author":"Oger F.","journal-title":"J. London Math. Soc."},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3618-1"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1969-126-4"},{"key":"rf16","volume-title":"The Theory of Groups","author":"Rotman J. J.","year":"1973"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61856-7"},{"key":"rf18","doi-asserted-by":"crossref","first-page":"203","DOI":"10.4064\/fm-41-2-203-271","volume":"41","author":"Szmielew W.","journal-title":"Fund. Math."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196703001286","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T15:30:57Z","timestamp":1704900657000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196703001286"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6]]},"references-count":18,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,6]]}},"alternative-id":["10.1142\/S0218196703001286"],"URL":"https:\/\/doi.org\/10.1142\/s0218196703001286","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,6]]}}}