{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T06:14:46Z","timestamp":1775628886206,"version":"3.50.1"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2476,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In [2] T. J. Carlson introduces an approach to ordinal notation systems which is based on the notion of \u03a3<jats:sub>1<\/jats:sub>-elementary substructure. We gave a detailed ordinal arithmetical analysis (see [7]) of the ordinal structure based on \u03a3<jats:sub>1<\/jats:sub>-elementarily as defined in [2]. This involved the development of an appropriate ordinal arithmetic that is based on a system of classical ordinal notations derived from Skolem hull operators, see [6]. In the present paper we establish an effective order isomorphism between the classical and the new system of ordinal notations using the results from [6] and [7]. Moreover, on the basis of a concept of relativization we develop mutual (relatively) elementary recursive assignments which are uniform with respect to the underlying relativization.<\/jats:p>","DOI":"10.2178\/jsl\/1185803630","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T11:24:48Z","timestamp":1198063488000},"page":"704-720","source":"Crossref","is-referenced-by-count":12,"title":["Assignment of ordinals to patterns of resemblance"],"prefix":"10.1017","volume":"72","author":[{"given":"Gunnar","family":"Wilken","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005429_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2006.07.004"},{"key":"S0022481200005429_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2006.07.003"},{"key":"S0022481200005429_ref003","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-46825-7","volume-title":"Proof theory. An introduction","volume":"1407","author":"Pohlers","year":"1989"},{"key":"S0022481200005429_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(00)00040-3"},{"key":"S0022481200005429_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050150"},{"key":"S0022481200005429_ref004","unstructured":"Wilken G. , \u03a31-elementarity and Skolem hull operators, Ph.D. thesis, University of M\u00fcnster, 2004."},{"key":"S0022481200005429_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-006-0010-6"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200005429","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T18:13:18Z","timestamp":1556734398000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200005429\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,6]]}},"alternative-id":["S0022481200005429"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1185803630","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,6]]}}}