Ali Enayat had asked whether two halves of Disjunctive Correctness ($\mathrm{\text{DC}}$) 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 $\mathrm{\text{PA}}$. The methods introduced here allow us to give a direct nonconservativeness proof for $\mathrm{\text{DC}}$.

中文翻译：

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分离正确性的两半

Ali Enayat 曾问过分离正确性的两半（$\mathrm{\text{直流电}}$) 因为组合真值谓词比皮亚诺算术 (PA) 保守。在本文中，我们证明了“每个真析取都有一个真析取”的原则等价于组合真谓词的有界归纳，因此它不是保守的。另一方面，逆向蕴涵“任何具有真析取的析取都是真的”可以保守地添加到$\mathrm{\text{功率放大器}}$. 这里介绍的方法允许我们给出直接的非保守性证明$\mathrm{\text{直流电}}$.