{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:54:43Z","timestamp":1777517683885,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2015,2,1]],"date-time":"2015-02-01T00:00:00Z","timestamp":1422748800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p>\n                    We investigate the set of \u03a0\n                    <jats:sup>1<\/jats:sup>\n                    <jats:sub>2<\/jats:sub>\n                    sentences which are \u03a0\n                    <jats:sup>1<\/jats:sup>\n                    <jats:sub>1<\/jats:sub>\n                    conservative over theories of second order arithmetic. We exhibit new elements of these sets and conclude that the sets are \u03a0\n                    <jats:sub>2<\/jats:sub>\n                    complete. Along the way, we show that, over the theory RCA\n                    <jats:sub>0<\/jats:sub>\n                    , induction for \u03a3\n                    <jats:sub>n<\/jats:sub>\n                    formulas has essentially no consequences for \u0394\n                    <jats:sub>n+1<\/jats:sub>\n                    formulas.\n                  <\/jats:p>","DOI":"10.3233\/com-150033","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T15:00:34Z","timestamp":1575298834000},"page":"57-68","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On maximum conservative extensions"],"prefix":"10.1177","volume":"4","author":[{"given":"Henry","family":"Towsner","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA. E-mail: htowsner@math.upenn.edu; Url: www.math.upenn.edu\/~htowsner"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,2,1]]},"container-title":["Computability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-150033","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-150033","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T16:03:12Z","timestamp":1777392192000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/COM-150033"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["10.3233\/COM-150033"],"URL":"https:\/\/doi.org\/10.3233\/com-150033","relation":{},"ISSN":["2211-3568","2211-3576"],"issn-type":[{"value":"2211-3568","type":"print"},{"value":"2211-3576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2]]}}}