{"title":"The two halves of disjunctive correctness","authors":"Cezary Cie'sli'nski, Mateusz Lelyk, Bartosz Wcislo","doi":"10.1142/s021906132250026x","DOIUrl":null,"url":null,"abstract":"Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic. In this article, we show that the principle\"every true disjunction has a true disjunct\"is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On the other hand, the converse implication\"any disjunction with a true disjunct is true\"can be conservatively added to PA. The methods introduced here allow us to give a direct nonconservativeness proof for DC.","PeriodicalId":50144,"journal":{"name":"Journal of Mathematical Logic","volume":"475 1","pages":"2250026:1-2250026:28"},"PeriodicalIF":0.9000,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s021906132250026x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 3
Abstract
Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic. In this article, we show that the principle"every true disjunction has a true disjunct"is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On the other hand, the converse implication"any disjunction with a true disjunct is true"can be conservatively added to PA. The methods introduced here allow us to give a direct nonconservativeness proof for DC.
Ali Enayat问组合真谓词的两半析取正确性(DC)是否在Peano算术上是保守的。在本文中，我们证明了“每个真析取都有一个真析取”的原理等价于组合真谓词的有界归纳法，因此它不是保守的。另一方面，逆向蕴涵“任何有真析取的析取都为真”可以保守地添加到PA中。本文介绍的方法使我们能够给出直流的直接非保守性证明。
期刊介绍：
The Journal of Mathematical Logic (JML) provides an important forum for the communication of original contributions in all areas of mathematical logic and its applications. It aims at publishing papers at the highest level of mathematical creativity and sophistication. JML intends to represent the most important and innovative developments in the subject.
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