{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T16:08:12Z","timestamp":1780934892103,"version":"3.54.1"},"reference-count":6,"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":[[2005,6]]},"abstract":"<jats:p> A Dedekind-finite set is said to be divisible by a natural number n if it can be partitioned into pieces of size n. We study several aspects of this notion, as well as the stronger notion of being partitionable into n pieces of equal size. Among our results are that the divisors of a Dedekind-finite set can consistently be any set of natural numbers (containing 1 but not 0), that a Dedekind-finite power of 2 cannot be divisible by 3, and that a Dedekind-finite set can be congruent modulo 3, to all of 0, 1, and 2 simultaneously. (In these results, 2 and 3 serve as typical examples; the full results are more general.) <\/jats:p>","DOI":"10.1142\/s0219061305000389","type":"journal-article","created":{"date-parts":[[2005,6,22]],"date-time":"2005-06-22T07:49:55Z","timestamp":1119426595000},"page":"49-85","source":"Crossref","is-referenced-by-count":2,"title":["DIVISIBILITY OF DEDEKIND FINITE SETS"],"prefix":"10.1142","volume":"05","author":[{"given":"DAVID","family":"BLAIR","sequence":"first","affiliation":[{"name":"Mathematics Department, University of Michigan, Ann Arbor, MI 48109\u20131109, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ANDREAS","family":"BLASS","sequence":"additional","affiliation":[{"name":"Mathematics Department, University of Michigan, Ann Arbor, MI 48109\u20131109, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"PAUL","family":"HOWARD","sequence":"additional","affiliation":[{"name":"Mathematics Department, Eastern Michigan University, Ypsilanti, MI 48197, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf2","first-page":"253","author":"Fraenkel A.","journal-title":"Sitzungsberichte Preu\u00dfischen Akad. Wiss. (Berlin) Phys.-Math. Kl."},{"key":"rf3","volume-title":"The Axiom of Choice","author":"Jech T.","year":"1973"},{"key":"rf4","first-page":"351","volume":"14","author":"Jech T.","journal-title":"Bull. Acad. Polon. Sci. S\u00e9r. Sci. Math. Astronom. Phys."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(81)90052-9"},{"key":"rf6","first-page":"299","volume":"19","author":"Lindenbaum A.","journal-title":"C. R. S\u00e9ances Soc. Sci. Lett. Varsovie, Classe III"},{"key":"rf7","doi-asserted-by":"crossref","first-page":"77","DOI":"10.4064\/fm-36-1-77-92","volume":"36","author":"Tarski A.","journal-title":"Fund. Math."}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061305000389","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:32:33Z","timestamp":1565080353000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061305000389"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6]]},"references-count":6,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2005,6]]}},"alternative-id":["10.1142\/S0219061305000389"],"URL":"https:\/\/doi.org\/10.1142\/s0219061305000389","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6]]}}}