{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:45:19Z","timestamp":1777535119974,"version":"3.51.4"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"NCN MAESTRO","award":["2019\/34\/A\/HS1\/00399"],"award-info":[{"award-number":["2019\/34\/A\/HS1\/00399"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>Ali Enayat had asked whether two halves of Disjunctive Correctness ([Formula: see text]) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, we show that the principle \u201cevery true disjunction has a true disjunct\u201d is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On the other hand, the converse implication \u201cany disjunction with a true disjunct is true\u201d can be conservatively added to [Formula: see text]. The methods introduced here allow us to give a direct nonconservativeness proof for [Formula: see text].<\/jats:p>","DOI":"10.1142\/s021906132250026x","type":"journal-article","created":{"date-parts":[[2022,8,8]],"date-time":"2022-08-08T03:29:30Z","timestamp":1659929370000},"source":"Crossref","is-referenced-by-count":4,"title":["The two halves of disjunctive correctness"],"prefix":"10.1142","volume":"23","author":[{"given":"Cezary","family":"Cie\u015bli\u0144ski","sequence":"first","affiliation":[{"name":"Faculty of Philosophy, University of Warsaw, Warszawa, Poland"}]},{"given":"Mateusz","family":"\u0141e\u0142yk","sequence":"additional","affiliation":[{"name":"Faculty of Philosophy, University of Warsaw, Warszawa, Poland"}]},{"given":"Bartosz","family":"Wcis\u0142o","sequence":"additional","affiliation":[{"name":"Institute of Philosophy, University of Gda\u0144sk, Gda\u0144sk, Poland"}]}],"member":"219","published-online":{"date-parts":[[2022,12,17]]},"reference":[{"key":"S021906132250026XBIB001","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1093\/mind\/fzq034","volume":"119","author":"Cie\u015bli\u0144ski C.","year":"2010","journal-title":"Mind"},{"key":"S021906132250026XBIB002","doi-asserted-by":"crossref","DOI":"10.1017\/9781108178600","volume-title":"The Epistemic Lightness of Truth. 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