{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T06:24:55Z","timestamp":1671085495986},"reference-count":7,"publisher":"Oxford University Press (OUP)","issue":"8","license":[{"start":{"date-parts":[[2022,11,26]],"date-time":"2022-11-26T00:00:00Z","timestamp":1669420800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,12,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We introduce Noetherian G\u00f6del logics, G\u00f6del logics where the set of truth values is a closed subset of $[0,1]$ containing $0$ and $1$ and without any infinite ascending sequences. There are infinitely many such logics, including the well-known logic $\\textsf {G}^\\downarrow $ whose set of truth values is $T_\\downarrow = \\{0\\}\\cup \\{1\/n:n\\in \\mathbb {N}\\setminus \\{0\\}\\}$. We compute the complexity of satisfiability and validity for each Noetherian G\u00f6del logic and, in particular, in the logic $\\textsf {G}^\\downarrow $. This yields optimal strengthening of the results of Baaz\u2013Leitsch\u2013Zach and H\u00e1jek<\/jats:p>","DOI":"10.1093\/logcom\/exac064","type":"journal-article","created":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T22:48:08Z","timestamp":1668725288000},"page":"1487-1503","source":"Crossref","is-referenced-by-count":0,"title":["Noetherian G\u00f6del logics"],"prefix":"10.1093","volume":"32","author":[{"given":"Juan Pablo","family":"Aguilera","sequence":"first","affiliation":[{"name":"Department of Mathematics , Ghent University, Krijgslaan 281, Gebouw S8, 9000 Gent, Belgium and Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria"}]},{"given":"Jan","family":"Byd\u017eovsk\u00fd","sequence":"additional","affiliation":[{"name":"Institute of Discrete Mathematics and Geometry , Vienna University of Technology, Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria"}]},{"given":"David","family":"Fern\u00e1ndez-Duque","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Ghent University, Krijgslaan 281, Gebouw S8, 9000 Gent, Belgium and Institute of Computer Science, Czech Academy of Sciences, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 271\/2, Prague, Czechia"}]}],"member":"286","published-online":{"date-parts":[[2022,11,26]]},"reference":[{"key":"2022121408225633500_ref1","article-title":"Incompleteness of a first-order G\u00f6del logic and some temporal logics of programs","author":"Baaz","year":"1996","journal-title":"Proceedings of CSL\u201995"},{"key":"2022121408225633500_ref2","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.apal.2007.03.001","article-title":"First-order G\u00f6del logics","volume":"147","author":"Baaz","year":"2007","journal-title":"Annals of Pure and Applied Logic"},{"key":"2022121408225633500_ref3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-11035-5","volume-title":"Admissible Sets and Structures. Perspectives in Mathematical Logic","author":"Barwise","year":"1975"},{"key":"2022121408225633500_ref4","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2307\/2964753","article-title":"A propositional calculus with denumerable matrix","volume":"24","author":"Dummett","year":"1959","journal-title":"The Journal of Symbolic Logic"},{"key":"2022121408225633500_ref5","first-page":"65","article-title":"Zum Intuitionistischen Aussagenkalk\u00fcl","volume":"69","author":"G\u00f6del","year":"1932","journal-title":"Anzeiger der Akademie der Wissenschaften in Wien"},{"key":"2022121408225633500_ref6","first-page":"435","article-title":"A non-arithmetical G\u00f6del logic","volume-title":"Logic Journal of the IGPL","author":"H\u00e1jek","year":"2005"},{"key":"2022121408225633500_ref7","article-title":"Springer Monographs in Mathematics","volume-title":"Set Theory","author":"Jech","year":"2003"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/32\/8\/1487\/47846335\/exac064.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/32\/8\/1487\/47846335\/exac064.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T11:11:19Z","timestamp":1671016279000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/32\/8\/1487\/6841328"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,26]]},"references-count":7,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,11,26]]},"published-print":{"date-parts":[[2022,12,9]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exac064","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,12]]},"published":{"date-parts":[[2022,11,26]]}}}