{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T08:44:44Z","timestamp":1775637884173,"version":"3.50.1"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8046,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that there exists a function <jats:italic>f<\/jats:italic> which reduces a given <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200023240_inline1\"\/> subset <jats:italic>P<\/jats:italic> of an internal set <jats:italic>X<\/jats:italic> of an <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub> saturated nonstandard universe to the set <jats:bold>WF<\/jats:bold> of well-founded trees possessing properties similar to those possessed by the standard part map. We use <jats:italic>f<\/jats:italic> to define the Lusin-Sierpi\u0144ski index of points in <jats:italic>X<\/jats:italic>, and prove the basic properties of that index using the classical properties of the Lusin-Sierpi\u0144ski index. An example of a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200023240_inline1\"\/> but not <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200023240_inline2\"\/> set is given.<\/jats:p>","DOI":"10.2307\/2275183","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:43:45Z","timestamp":1146941025000},"page":"172-178","source":"Crossref","is-referenced-by-count":4,"title":["Lusin-Sierpi\u0144ski index for the internal sets"],"prefix":"10.1017","volume":"57","author":[{"given":"Bo\u0161ko","family":"\u017divaljevi\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200023240_ref005","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-6.3.491"},{"key":"S0022481200023240_ref007","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-12.2.213"},{"key":"S0022481200023240_ref001","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1979-066-0"},{"key":"S0022481200023240_ref003","first-page":"1167","volume":"54","author":"Keisler","year":"1989","journal-title":"Descriptive set theory over a hyperfinite set"},{"key":"S0022481200023240_ref006","doi-asserted-by":"publisher","DOI":"10.4064\/fm-71-3-263-271"},{"key":"S0022481200023240_ref004","volume-title":"Descriptive set theory","author":"Moschovakis","year":"1980"},{"key":"S0022481200023240_ref002","unstructured":"Henson C. W. , Private communication."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200023240","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T18:32:41Z","timestamp":1558031561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200023240\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,3]]}},"alternative-id":["S0022481200023240"],"URL":"https:\/\/doi.org\/10.2307\/2275183","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}