{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:09:19Z","timestamp":1775470159109,"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":1107,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2011,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Improving on a result of Arana, we construct an effective family (<jats:italic>\u03c6<jats:sub>r<\/jats:sub><\/jats:italic> \u2223 <jats:italic>r<\/jats:italic> \u03f5 \u211a \u2229 [0,1]) of \u03a3<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>-conservative \u03a0<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> sentences, increasing in strength as <jats:italic>r<\/jats:italic> decreases, with the property that \u00ac<jats:italic>\u03c6<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic><\/jats:sub> is \u03a0<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>-conservative over PA + <jats:italic>\u03c6<jats:sub>q<\/jats:sub><\/jats:italic> whenever <jats:italic>p<\/jats:italic> &lt; <jats:italic>q<\/jats:italic>. We also construct a family of \u03a3<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> sentences with properties as above except that the roles of \u03a3<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> and \u03a0<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> are reversed. The latter result allows to re-obtain an unpublished result of Solovay, the presence of a subset order-isomorphic to the reals in every non-trivial end-segment of every branch of the <jats:italic>E<\/jats:italic>-tree, and to generalize it to analogues of the <jats:italic>E<\/jats:italic>-tree at higher levels of the arithmetical hierarchy.<\/jats:p>","DOI":"10.2178\/jsl\/1294171003","type":"journal-article","created":{"date-parts":[[2011,1,4]],"date-time":"2011-01-04T20:22:35Z","timestamp":1294172555000},"page":"341-347","source":"Crossref","is-referenced-by-count":2,"title":["A theorem on partial conservativity in arithmetic"],"prefix":"10.1017","volume":"76","author":[{"given":"Per","family":"Lindstr\u00f6m","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002127_ref006","unstructured":"V. Yu. Shavrukov , Dense chains of \u03a3n sentences with strong conservativity properties, in preparation."},{"key":"S0022481200002127_ref005","unstructured":"Misercque D. , Sur le treillis des formu\u00e9es fermies untverselles de l'arithm\u00e9tique de Peano, Ph.D. thesis, Universit\u00e9 Libre de Bruxelles, 1985."},{"key":"S0022481200002127_ref004","volume-title":"Aspects of incompleteness","volume":"10","author":"Lindstr\u00f6m","year":"2003"},{"key":"S0022481200002127_ref003","doi-asserted-by":"publisher","DOI":"10.4064\/fm-92-3-223-245"},{"key":"S0022481200002127_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1979-0539907-7"},{"key":"S0022481200002127_ref007","unstructured":"Shavrukov V. Yu. and Solovay R. M. , Branches of the E-tree and jump pseudo-hierarchies, in preparation."},{"key":"S0022481200002127_ref001","first-page":"1","volume":"69","author":"Arana","year":"2004","journal-title":"Arithmetical independence results using higher recursion theory"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002127","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T19:24:25Z","timestamp":1556393065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002127\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["S0022481200002127"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1294171003","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}