{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T10:40:48Z","timestamp":1693824048579},"reference-count":5,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2021,1,15]],"date-time":"2021-01-15T00:00:00Z","timestamp":1610668800000},"content-version":"vor","delay-in-days":45,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Regarding strictly monadic second\u2010order logic (SMSOL), which is the fragment of monadic second\u2010order logic in which all predicate constants are unary and there are no function symbols, we show that a standard deductive system with full comprehension is sound and complete with respect to standard semantics. This result is achieved by showing that in the case of SMSOL, the truth value of any formula in a faithful identity\u2010standard Henkin structure is preserved when the structure is \u201cstandardized\u201d; that is, the predicate domain is expanded into the set of all unary relations. In addition, we obtain a simpler proof of the decidability of\u00a0SMSOL.<\/jats:p>","DOI":"10.1002\/malq.201900046","type":"journal-article","created":{"date-parts":[[2021,1,15]],"date-time":"2021-01-15T23:48:20Z","timestamp":1610754500000},"page":"438-447","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the completeness and the decidability of strictly monadic second\u2010order logic"],"prefix":"10.1002","volume":"66","author":[{"given":"Kento","family":"Takagi","sequence":"first","affiliation":[{"name":"Department of Mathematical and Computing Science Tokyo Institute of Technology 2\u201012\u20101, Ookayama, Meguro Tokyo 152\u20108552 Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryo","family":"Kashima","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computing Science Tokyo Institute of Technology 2\u201012\u20101, Ookayama, Meguro Tokyo 152\u20108552 Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,1,15]]},"reference":[{"key":"e_1_2_7_2_1","volume-title":"Solvable Cases of the Decision Problem","author":"Ackermann W.","year":"1954"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804076"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33475-7_22"},{"key":"e_1_2_7_5_1","volume-title":"Foundations without Foundationalism: A Case for Second\u2010Order Logic","author":"Shapiro S.","year":"1991"},{"key":"e_1_2_7_6_1","unstructured":"K.TakagiandR.Kashima On the completeness and the decidability of strictly monadic second\u2010order logic Research Reports on Mathematical and Computing Sciences C\u2010286 (Tokyo Institute of Technology 2019)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201900046","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.201900046","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201900046","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T16:32:56Z","timestamp":1693758776000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201900046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12]]},"references-count":5,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1002\/malq.201900046"],"URL":"https:\/\/doi.org\/10.1002\/malq.201900046","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12]]},"assertion":[{"value":"2019-06-17","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-04-27","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}