{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T18:13:05Z","timestamp":1648836785862},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":2512,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2007,3]]},"abstract":"<jats:p>Full proofs of the G\u00f6del incompleteness theorems are highly intricate affairs. Much of the intricacy lies in the details of setting up and checking the properties of a coding system representing the syntax of an object language (typically, that of arithmetic) within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs of G\u00f6del's theorems without getting mired in syntactic or computational details. One of the most important of these efforts was made by L\u00f6b [8] in connection with his analysis of sentences asserting their own provability. L\u00f6b formulated three conditions (now known as the <jats:italic>Hilbert-Bernays-L\u00f6b<\/jats:italic> derivability conditions), on the provability predicate in a formal system which are jointly sufficient to yield the G\u00f6del's second incompleteness theorem for it. A key role in L\u00f6b's analysis is played by (a special case of) what later became known as the <jats:italic>diagonalization<\/jats:italic> or <jats:italic>fixed point<\/jats:italic> property of formal systems, a property which had already, in essence, been exploited by G\u00f6del in his original proofs of the incompleteness theorems. The fixed point property plays a central role in Lawvere's [7] category-theoretic account of incompleteness phenomena (see also [10]).<\/jats:p>","DOI":"10.2178\/bsl\/1174668216","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:55:07Z","timestamp":1197557707000},"page":"21-30","source":"Crossref","is-referenced-by-count":1,"title":["Incompleteness in a General Setting"],"prefix":"10.1017","volume":"13","author":[{"given":"John L.","family":"Bell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S107989860000233X_ref005","volume-title":"The logic of provability","author":"Boolos","year":"1995"},{"key":"S107989860000233X_ref010","unstructured":"Yanofsky N. , A universal approach to self-referential paradoxes, incompleteness and fixed points, this Bulletin, vol. 9 (2003), no. 3, pp. 362\u2013386."},{"key":"S107989860000233X_ref007","first-page":"134","volume-title":"Battelle Institute Conference, Seattle, Washington, 1968","author":"Lawvere","year":"1969"},{"key":"S107989860000233X_ref003","volume-title":"A course in mathematical logic","author":"Bell","year":"1977"},{"key":"S107989860000233X_ref004","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/103.409.1"},{"key":"S107989860000233X_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/2266895"},{"key":"S107989860000233X_ref002","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198568520.001.0001"},{"key":"S107989860000233X_ref006","volume-title":"Computability and logic","author":"Boolos","year":"1974"},{"key":"S107989860000233X_ref001","volume-title":"Toposes and local set theories","author":"Bell","year":"1988"},{"key":"S107989860000233X_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71123-6"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S107989860000233X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T00:09:31Z","timestamp":1556755771000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S107989860000233X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,3]]}},"alternative-id":["S107989860000233X"],"URL":"https:\/\/doi.org\/10.2178\/bsl\/1174668216","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,3]]}}}