具有命题重言式和无量词正确性的组合真

IF 0.4 4区数学 Q4 LOGIC

Archive for Mathematical Logic Pub Date : 2023-10-06 DOI:10.1007/s00153-023-00893-3

Bartosz Wcisło

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引用次数: 1

摘要

在Cieśliński (J Philos Logic 39:325-337, 2010)中，Cieśliński提出了命题重言式为真这一附加公理的组合真理论在Peano算术上是否保守的问题。我们提供了这个问题的部分答案，表明如果我们额外假设真值谓词与无量词句子上的算术真值一致，则所得理论与组合真值谓词的$$\Delta _0$$ Δ 0 -归纳一样强，因此是非保守的。另一方面，可以用一个常规论证来证明，无量词正确性原则本身是保守的。

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Compositional truth with propositional tautologies and quantifier-free correctness

Abstract In Cieśliński (J Philos Logic 39:325–337, 2010), Cieśliński asked whether compositional truth theory with the additional axiom that all propositional tautologies are true is conservative over Peano Arithmetic. We provide a partial answer to this question, showing that if we additionally assume that truth predicate agrees with arithmetical truth on quantifier-free sentences, the resulting theory is as strong as $$\Delta _0$$ Δ 0 -induction for the compositional truth predicate, hence non-conservative. On the other hand, it can be shown with a routine argument that the principle of quantifier-free correctness is itself conservative.

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来源期刊

Archive for Mathematical Logic 数学-数学

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期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.