{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T04:23:07Z","timestamp":1783484587451,"version":"3.55.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":16506,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1969,1]]},"abstract":"<jats:p>Why the Post-Kleene arithmetical hierarchy of degrees of (recursive) unsolvability was extended into the transfinite is not clear. Perhaps it was thought that if a hierarchy of sufficiently fine structure could be described that would include all sets of integers, some light might be thrown on the Continuum Hypothesis, and its truth or falsity possibly even ascertained. There is also some evidence in the 1955 papers of Kleene (cf. Kleene [2], [3], [4]) that it was once hoped that a theorem for the analytical hierarchy analogous to the result of Post and Kleene<\/jats:p>","DOI":"10.2307\/2271357","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:50:27Z","timestamp":1146948627000},"page":"497-513","source":"Crossref","is-referenced-by-count":33,"title":["Degrees of unsolvability of constructible sets of integers"],"prefix":"10.1017","volume":"33","author":[{"given":"George","family":"Boolos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hilary","family":"Putnam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200109107_ref009","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1955-0070594-4"},{"key":"S0022481200109107_ref008","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200109107_ref003","unstructured":"Boyd R. , Hensel G. , and Putnam H. , [1] On an intrinsic characterization of the ramified analytic hierarchy (to appear)."},{"key":"S0022481200109107_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1957-0091243-2"},{"key":"S0022481200109107_ref006","first-page":"571","article-title":"Proof of Mostowski's conjecture","volume":"8","author":"Gandy","year":"1960","journal-title":"Bulletin de l' Acad\u00e9mie Polonaise des Sciences, S\u00e9rie des Sciences, Mathematiques, Astronomiques"},{"key":"S0022481200109107_ref007","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.25.4.220"},{"key":"S0022481200109107_ref002","unstructured":"Boolos G. 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