{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T05:11:04Z","timestamp":1700543464558},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T00:00:00Z","timestamp":1653436800000},"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":[[2023,1,20]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study propositional and first-order G\u00f6del logics over infinitary languages, which are motivated semantically by corresponding interpretations into the unit interval $[0,1]$. We provide infinitary Hilbert-style calculi for the particular (propositional and first-order) cases with con-\/disjunctions of countable length and prove corresponding completeness theorems by extending the usual Lindenbaum\u2013Tarski construction to the infinitary case for a respective algebraic semantics via complete linear Heyting algebras. We provide infinitary hypersequent calculi and prove corresponding cut-elimination theorems in the Sch\u00fctte\u2013Tait style. Initial observations are made regarding truth-value sets other than $[0,1]$.<\/jats:p>","DOI":"10.1093\/logcom\/exac040","type":"journal-article","created":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T19:11:08Z","timestamp":1651691468000},"page":"1-46","source":"Crossref","is-referenced-by-count":0,"title":["On infinitary G\u00f6del logics"],"prefix":"10.1093","volume":"33","author":[{"given":"Nicholas","family":"Pischke","sequence":"first","affiliation":[{"name":"Department of Mathematics , Technische Universit\u00e4t Darmstadt, Schlossgartenstra\u00dfe 7, 64289, Darmstadt, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,5,25]]},"reference":[{"key":"2023022314483693000_","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/978-3-662-52921-8_2","article-title":"Compactness in infinitary G\u00f6del logics","volume-title":"Logic, Language, Information, and Computation, 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