{"title":"具有命题正确性的组合真理的饱和特性","authors":"Bartosz Wcisło","doi":"10.1016/j.apal.2024.103512","DOIUrl":null,"url":null,"abstract":"<div><p>It is an open question whether compositional truth with the principle of propositional soundness: “All arithmetical sentences which are propositional tautologies are true” is conservative over Peano Arithmetic. In this article, we show that the principle of propositional soundness imposes some saturation-like properties on the truth predicate, thus showing significant limitations to the possible conservativity proof.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 2","pages":"Article 103512"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168007224001167/pdfft?md5=93f2e704b024dfc73e7a30a7ab95c178&pid=1-s2.0-S0168007224001167-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Saturation properties for compositional truth with propositional correctness\",\"authors\":\"Bartosz Wcisło\",\"doi\":\"10.1016/j.apal.2024.103512\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is an open question whether compositional truth with the principle of propositional soundness: “All arithmetical sentences which are propositional tautologies are true” is conservative over Peano Arithmetic. In this article, we show that the principle of propositional soundness imposes some saturation-like properties on the truth predicate, thus showing significant limitations to the possible conservativity proof.</p></div>\",\"PeriodicalId\":50762,\"journal\":{\"name\":\"Annals of Pure and Applied Logic\",\"volume\":\"176 2\",\"pages\":\"Article 103512\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0168007224001167/pdfft?md5=93f2e704b024dfc73e7a30a7ab95c178&pid=1-s2.0-S0168007224001167-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0168007224001167\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168007224001167","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
Saturation properties for compositional truth with propositional correctness
It is an open question whether compositional truth with the principle of propositional soundness: “All arithmetical sentences which are propositional tautologies are true” is conservative over Peano Arithmetic. In this article, we show that the principle of propositional soundness imposes some saturation-like properties on the truth predicate, thus showing significant limitations to the possible conservativity proof.
期刊介绍：
The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.
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