{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:05:44Z","timestamp":1772445944580,"version":"3.50.1"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2013,2,1]],"date-time":"2013-02-01T00:00:00Z","timestamp":1359676800000},"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":[[2013,2]]},"abstract":"<jats:p> We construct a computable, computably categorical field of infinite transcendence degree over the rational numbers, using the Fermat polynomials and assorted results from algebraic geometry. We also show that this field has an intrinsically computable (infinite) transcendence basis. <\/jats:p>","DOI":"10.3233\/com-13017","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T15:00:10Z","timestamp":1575298810000},"page":"51-65","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Computably Categorical Fields via Fermat\u2019s Last Theorem"],"prefix":"10.1177","volume":"2","author":[{"given":"Russell","family":"Miller","sequence":"first","affiliation":[{"name":"Department of Mathematics, Queens College \u2013 C.U.N.Y. 65-30 Kissena Blvd. Flushing, New York 11367 U.S.A. Ph.D. Programs in Mathematics & Computer Science, C.U.N.Y. Graduate Center, 365 Fifth Avenue, New York, New York 10016 U.S.A. Russell.Miller@qc.cuny.edu qcpages.qc.cuny.edu\/~rmiller"}]},{"given":"Hans","family":"Schoutens","sequence":"additional","affiliation":[{"name":"Department of Mathematics, New York City College of Technology, 300 Jay Street Brooklyn, New York 11201 U.S.A. Ph.D. Program in Mathematics, C.U.N.Y. Graduate Center, 365 Fifth Avenue, New York, New York 10016 U.S.A. hschoutens@citytech.cuny.edu, websupport1.citytech.cuny.edu\/faculty\/hschoutens\/"}]}],"member":"179","published-online":{"date-parts":[[2013,2,1]]},"container-title":["Computability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-13017","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/COM-13017","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T12:22:21Z","timestamp":1757420541000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/COM-13017"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["10.3233\/COM-13017"],"URL":"https:\/\/doi.org\/10.3233\/com-13017","relation":{},"ISSN":["2211-3568","2211-3576"],"issn-type":[{"value":"2211-3568","type":"print"},{"value":"2211-3576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2]]}}}