{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T22:49:18Z","timestamp":1648939758977},"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":11607,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:p>Flipping properties were introduced in set theory by Abramson, Harrington, Kleinberg and Zwicker [1]. Here we consider them in the context of arithmetic and link them with combinatorial properties of initial segments of nonstandard models studied in [3]. As a corollary we obtain independence resutls involving flipping properties.<\/jats:p><jats:p>We follow the notation of the author and Paris in [3] and [2], and assume some knowledge of [3]. <jats:italic>M<\/jats:italic> will denote a countable nonstandard model of <jats:italic>P<\/jats:italic> (Peano arithmetic) and <jats:italic>I<\/jats:italic> will be a proper initial segment of <jats:italic>M<\/jats:italic>. We denote by <jats:italic>N<\/jats:italic> the standard model or the standard part of <jats:italic>M. X<\/jats:italic> \u2191 <jats:italic>I<\/jats:italic> will mean that <jats:italic>X<\/jats:italic> is unbounded in <jats:italic>I<\/jats:italic>. If <jats:italic>X<\/jats:italic> \u2286 <jats:italic>M<\/jats:italic> is coded in <jats:italic>M<\/jats:italic> and <jats:italic>M<\/jats:italic> \u227a <jats:italic>K<\/jats:italic>, let <jats:italic>X<jats:sup>(K)<\/jats:sup><\/jats:italic> be the subset of <jats:italic>K<\/jats:italic> coded in <jats:italic>K<\/jats:italic> by the element which codes <jats:italic>X<\/jats:italic> in <jats:italic>M<\/jats:italic>. So <jats:italic>X<jats:sup>(K)<\/jats:sup><\/jats:italic> \u22c2 <jats:italic>M<\/jats:italic> = <jats:italic>X<\/jats:italic>.<\/jats:p><jats:p>Recall that <jats:italic>M<\/jats:italic> \u227a<jats:sup><jats:italic>I<\/jats:italic><\/jats:sup><jats:italic>K<\/jats:italic> (<jats:italic>K<\/jats:italic> is an <jats:italic>I<\/jats:italic>-extension of <jats:italic>M<\/jats:italic>) if <jats:italic>M<\/jats:italic> \u227a <jats:italic>K<\/jats:italic> and for some <jats:italic>c<\/jats:italic><jats:italic>\u2208<\/jats:italic><jats:italic>K<\/jats:italic>,<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200044339_eqnU01\" \/><\/jats:disp-formula><\/jats:p><jats:p>In [3] regular and strong initial segments are defined, and among other things it is shown that <jats:italic>I<\/jats:italic> is regular if and only if there exists an <jats:italic>I<\/jats:italic>-extension of <jats:italic>M<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2273151","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:59:42Z","timestamp":1146952782000},"page":"416-422","source":"Crossref","is-referenced-by-count":4,"title":["Flipping properties in arithmetic"],"prefix":"10.1017","volume":"47","author":[{"given":"L. A. S.","family":"Kirby","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044339_ref006","first-page":"312","volume-title":"Proceedings of the 1979 Karpacz Conference","author":"Paris"},{"key":"S0022481200044339_ref005","first-page":"725","volume":"43","author":"Paris","year":"1978","journal-title":"Some independence results for Peano arithmetic"},{"key":"S0022481200044339_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0067653"},{"key":"S0022481200044339_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(77)90005-5"},{"key":"S0022481200044339_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72003-2"},{"key":"S0022481200044339_ref002","unstructured":"Kirby L. A. S. , Ph. D. Thesis, Manchester, 1977."},{"key":"S0022481200044339_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01117472"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200044339","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T21:16:11Z","timestamp":1558732571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200044339\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["S0022481200044339"],"URL":"https:\/\/doi.org\/10.2307\/2273151","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]}}}