{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,26]],"date-time":"2023-08-26T14:12:48Z","timestamp":1693059168562},"reference-count":24,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2022,2,6]],"date-time":"2022-02-06T00:00:00Z","timestamp":1644105600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2022,5]]},"abstract":"Abstract<\/jats:title>There is an extensive literature related to the algebraization of first\u2010order logic. But the algebraization of full second\u2010order logic, or Henkin\u2010type second\u2010order logic, has hardly been researched. The question arises: what kind of set algebra is the algebraic version of a Henkin\u2010type model of second\u2010order logic? The question is investigated within the framework of the theory of cylindric algebras. The answer is: a kind of cylindric\u2010relativized diagonal restricted set algebra. And the class of the subdirect products of these set algebras is the algebraization of Henkin\u2010type second\u2010order logic. It is proved that the algebraization of a complete calculus of the Henkin\u2010type second\u2010order logic is a class of a kind of diagonal restricted cylindric algebras. Furthermore, the connection with the non\u2010standard enlargements of standard complete second\u2010order structures is\u00a0investigated.<\/jats:p>","DOI":"10.1002\/malq.202100057","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T03:39:08Z","timestamp":1644205148000},"page":"149-158","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the algebraization of Henkin\u2010type second\u2010order logic"],"prefix":"10.1002","volume":"68","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-6652-2344","authenticated-orcid":false,"given":"Mikl\u00f3s","family":"Ferenczi","sequence":"first","affiliation":[{"name":"Budapest University of Technology and Economics Institute of Mathematics 1111 Budapest, Egry J\u00f3zsef u.\u00a01 Hungary"}]}],"member":"311","published-online":{"date-parts":[[2022,2,6]]},"reference":[{"issue":"3","key":"e_1_2_5_2_1","first-page":"444","article-title":"Cylindric and polyadic algebras of sentences","volume":"52","author":"Amer M.","year":"2012","journal-title":"Math. 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B.","year":"2001"},{"key":"e_1_2_5_10_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2011-05332-8"},{"key":"e_1_2_5_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201100109"},{"key":"e_1_2_5_12_1","first-page":"21","volume-title":"Boolean Logics, Expressions and Theories: An Overview","author":"Ferenczi M.","year":"2020"},{"key":"e_1_2_5_13_1","volume-title":"Logic for Computer Science","author":"Gallier J. 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