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Math. Logic"],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In Cie\u015bli\u0144ski (J Philos Logic 39:325\u2013337, 2010), Cie\u015bli\u0144ski asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this question, showing that if we additionally assume that truth predicate agrees with arithmetical truth on quantifier-free sentences, the resulting theory is as strong as <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\Delta _0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u0394<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-induction for the compositional truth predicate, hence non-conservative. On the other hand, it can be shown with a routine argument that the principle of quantifier-free correctness is itself conservative.\n<\/jats:p>","DOI":"10.1007\/s00153-023-00893-3","type":"journal-article","created":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T18:02:19Z","timestamp":1696615339000},"page":"239-257","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Compositional truth with propositional tautologies and quantifier-free correctness"],"prefix":"10.1007","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5970-5123","authenticated-orcid":false,"given":"Bartosz","family":"Wcis\u0142o","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,6]]},"reference":[{"key":"893_CR1","doi-asserted-by":"publisher","first-page":"283","DOI":"10.4153\/CMB-1981-045-3","volume":"24","author":"H Kotlarski","year":"1981","unstructured":"Kotlarski, H., Krajewski, S., Lachlan, A.: Construction of satisfaction classes for nonstandard models. 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