The two halves of disjunctive correctness

被引：6

作者：

Cieslinski, Cezary ^{[1
]}

Lelyk, Mateusz ^{[1
]}

Wcislo, Bartosz ^{[2
]}

机构：

[1] Univ Warsaw, Fac Philosophy, Warsaw, Poland

[2] Univ Gdansk, Inst Philosophy, Gdansk, Poland

来源：

JOURNAL OF MATHEMATICAL LOGIC | 2023年 / 23卷 / 02期

关键词：

Axiomatic truth theories; truth predicate; disjunctive correctness; Tarski boundary; satisfaction classes; COMPOSITIONAL TRUTH;

D O I：

10.1142/S021906132250026X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, 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.

引用

页数：28

共 24 条

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