圆锥上“算术-递归”的性质

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2020-11-20 DOI:10.1142/s0219061321500215

U. Andrews, M. Harrison-Trainor, N. Schweber

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引用次数: 0

摘要

我们说一个理论[公式:见文]满足算术-递归，如果任何[公式:见文]的[公式:见文]-可计算模型有一个[公式:见文]-可计算副本;也就是说，[公式:见文本]的模型满足一种跳跃反转。我们给出了一个非平凡地满足算术-递归的理论的例子，并证明了在锥上满足算术-递归的理论正是那些具有可数多个[公式:见文本]-来回类型的理论。

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The property "arithmetic-is-recursive" on a cone

We say that a theory [Formula: see text] satisfies arithmetic-is-recursive if any [Formula: see text]-computable model of [Formula: see text] has an [Formula: see text]-computable copy; that is, the models of [Formula: see text] satisfy a sort of jump inversion. We give an example of a theory satisfying arithmetic-is-recursive non-trivially and prove that the theories satisfying arithmetic-is-recursive on a cone are exactly those theories with countably many [Formula: see text]-back-and-forth types.

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来源期刊

Journal of Mathematical Logic MATHEMATICS-LOGIC

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

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.