{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:28:51Z","timestamp":1761611331479},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2010,2,1]],"date-time":"2010-02-01T00:00:00Z","timestamp":1264982400000},"content-version":"unspecified","delay-in-days":2588,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2003]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle\u2044ZF, building on a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the formalization unusually long, and not entirely satisfactory: two parts of the proof do not fit together. It seems impossible to solve these problems without formalizing the metatheory. However, the present development follows a standard textbook, Kenneth Kunen's<jats:italic>Set theory: an introduction to independence proofs<\/jats:italic>, and could support the formalization of further material from that book. It also serves as an example of what to expect when deep mathematics is formalized.<\/jats:p>","DOI":"10.1112\/s1461157000000449","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T11:41:45Z","timestamp":1375789305000},"page":"198-248","source":"Crossref","is-referenced-by-count":15,"title":["The Relative Consistency of the Axiom of Choice Mechanized Using Isabelle\u2044zf"],"prefix":"10.1112","volume":"6","author":[{"given":"Lawrence C.","family":"Paulson","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000000449_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/BF00881873"},{"key":"S1461157000000449_ref010","volume-title":"Introduction to mathematical logic","author":"Mendelson","year":"1997"},{"key":"S1461157000000449_ref018","doi-asserted-by":"crossref","unstructured":"18 Paulson Lawrence C. , \u2018The reflection theorem: a study in meta-theoretic reasoning\u2019, [22] 377\u2013391.","DOI":"10.1007\/3-540-45620-1_31"},{"key":"S1461157000000449_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45949-9"},{"key":"S1461157000000449_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45620-1"},{"key":"S1461157000000449_ref020","first-page":"235\u2019308","volume-title":"Second Scandinavian Logic Symposium","author":"Prawitz","year":"1971"},{"key":"S1461157000000449_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BF00248324"},{"key":"S1461157000000449_ref009","volume-title":"Set theory: an introduction to independence proofs","author":"Kunen","year":"1980"},{"key":"S1461157000000449_ref007","volume-title":"Naive set theory","author":"Halmos","year":"1960"},{"key":"S1461157000000449_ref003","volume-title":"Kurt G\u00f6del: collected works","volume":"II","author":"Feferman","year":"1990"},{"key":"S1461157000000449_ref017","doi-asserted-by":"crossref","first-page":"187","DOI":"10.7551\/mitpress\/5641.003.0013","volume-title":"Proof, language, and interaction: essays in honor of Robin Milner","author":"Paulson","year":"2000"},{"key":"S1461157000000449_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48256-3_11"},{"key":"S1461157000000449_ref004","first-page":"26","volume-title":"The consistency of the axiom of choice and of the generalized continuum hypothesis","volume":"[3]","author":"G\u00f6del","year":"1938"},{"key":"S1461157000000449_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/1385-7258(72)90034-0"},{"key":"S1461157000000449_ref005","first-page":"33","volume-title":"The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory","volume":"[3]","author":"G\u00f6del","year":"1940"},{"key":"S1461157000000449_ref016","doi-asserted-by":"publisher","DOI":"10.1109\/CSFW.1997.596788"},{"key":"S1461157000000449_ref006","first-page":"27","volume-title":"Consistency proof for the generalized continuum hypothesis","volume":"[3]","author":"G\u00f6del","year":"1939"},{"key":"S1461157000000449_ref014","article-title":"Isabelle: a generic theorem prover","volume":"828","author":"Paulson","year":"1994","journal-title":"Lecture Notes in Comput. 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