{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:04:48Z","timestamp":1700006688173},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2008,1,30]],"date-time":"2008-01-30T00:00:00Z","timestamp":1201651200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A version of Birkhoff's theorem is proved by constructive, predicative, methods. The version we prove has two conditions more than the classical one. First, the class considered is assumed to contain a generic family, which is defined to be a set\u2010indexed family of algebras such that if an identity is valid in every algebra of this family, it is valid in every algebra of the class. Secondly, the class is assumed to be closed under inductive limits. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710023","type":"journal-article","created":{"date-parts":[[2008,1,30]],"date-time":"2008-01-30T14:16:15Z","timestamp":1201702575000},"page":"27-34","source":"Crossref","is-referenced-by-count":0,"title":["A constructive version of Birkhoff's theorem"],"prefix":"10.1002","volume":"54","author":[{"given":"Jesper","family":"Carlstr\u00f6m","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2008,1,30]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100013463"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"S.Burris andH. P.Sankappanavar A Course in Universal Algebra (Springer 1981).","DOI":"10.1007\/978-1-4613-8130-3"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"G.Gr\u00e4tzer Universal Algebra second edition (Springer 1979).","DOI":"10.1007\/978-0-387-77487-9"},{"key":"e_1_2_1_5_2","unstructured":"E.Bishop Foundations of Constructive Analysis (McGraw\u2010Hill Book Co. 1967)."},{"key":"e_1_2_1_6_2","unstructured":"T.Streicher Realizability. Lecture notes (2004\/05). Available athttp:\/\/www.mathematik.tu\u2010darmstadt.de\/\u223cstreicher\/"},{"key":"e_1_2_1_7_2","unstructured":"A.Bauer The realizability approach to computable analysis and topology. Ph.D. thesis School of Computer Science Carnegie Mellon University (2000). Available athttp:\/\/andrej.com\/thesis\/"},{"key":"e_1_2_1_8_2","unstructured":"B.Nordstr\u00f6m K.Petersson andJ.Smith Programming in Martin\u2010L\u00f6f's Type Theory (Oxford University Press 1990). Available athttp:\/\/www.cs.chalmers.se\/Cs\/Research\/Logic\/book\/"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"J.Carlstr\u00f6m Subsets quotients and partial functions in Martin\u2010L\u00f6f's type theory. In: Types for Proofs and Programs Second International Workshop TYPES 2002 Berg en Dal The Netherlands April 24\u201328 2002 Selected Papers (H. Geuvers and F. Wiedijk eds.). Lecture Notes in Computer Science 2646 pp. 78\u201394 (Springer 2003).","DOI":"10.1007\/3-540-39185-1_5"},{"key":"e_1_2_1_10_2","unstructured":"J.Carlstr\u00f6m Formalized limits and colimits of setoids. Technical Report 9 Department of Mathematics Stockholm University (2003). Available athttp:\/\/www.math.su.se\/\u223cjesper\/research\/limitsinsetoid\/"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710023","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T17:52:18Z","timestamp":1699984338000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,30]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["10.1002\/malq.200710023"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710023","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,30]]}}}