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Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: <jats:italic>classical systems<\/jats:italic> (i.e., systems based on classical logic) and <jats:italic>nonclassical systems<\/jats:italic> (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227\u2013257, 2018), shows that there is a sense in which classical and nonclassical theories (in suitable variants) have the same models.<\/jats:p>","DOI":"10.1007\/s11225-022-10016-3","type":"journal-article","created":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T19:39:21Z","timestamp":1665862761000},"page":"83-111","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Notes on Models of (Partial) Kripke\u2013Feferman Truth"],"prefix":"10.1007","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3103-8568","authenticated-orcid":false,"given":"Luca","family":"Castaldo","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,15]]},"reference":[{"issue":"3","key":"10016_CR1","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1305\/ndjfl\/1040511343","volume":"35","author":"H Aoyama","year":"1994","unstructured":"Aoyama, H., The strong completeness of a system based on Kleene\u2019s strong three-valued logic, Notre Dame Journal of Formal Logic 35(3):355\u2013368, 1994.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"10016_CR2","doi-asserted-by":"crossref","unstructured":"Arai, T., Ordinal Analysis with an Introduction to Proof Theory, vol. 8 of Logic in Asia: Studia Logica Library, Springer, 2020.","DOI":"10.1007\/978-981-15-6459-8"},{"key":"10016_CR3","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/978-3-7908-1769-0_5","volume-title":"Beyond Two: Theory and Applications of Multiple-Valued Logic","author":"A Avron","year":"2003","unstructured":"Avron, A., Classical Gentzen-type methods in propositional many-valued logics, in M. 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