鸽子洞原理在超算术约简下的弱点

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2019-05-21 DOI:10.1142/S0219061321500136

B. Monin, Ludovic Patey

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引用次数: 4

摘要

2分区的无限鸽子洞原理([公式:见文])断言存在，对于每一个集合[公式:见文]，一个无限子集[公式:见文]或它的补。本文从可计算理论的角度研究了无限鸽子洞原理。我们特别证明了[公式:见文本]对于算术和超算术约简来说，承认强锥回避。我们也证明了对于每一个[公式:见文]集合，它的一个无穷低[公式:见文]子集或它的补集的存在性。这就回答了王的一个问题。为此，我们设计了一个新的强迫概念，它推广了Cholak等人的第一次和第二次跳跃控制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The weakness of the pigeonhole principle under hyperarithmetical reductions

The infinite pigeonhole principle for 2-partitions ([Formula: see text]) asserts the existence, for every set [Formula: see text], of an infinite subset of [Formula: see text] or of its complement. In this paper, we study the infinite pigeonhole principle from a computability-theoretic viewpoint. We prove in particular that [Formula: see text] admits strong cone avoidance for arithmetical and hyperarithmetical reductions. We also prove the existence, for every [Formula: see text] set, of an infinite low[Formula: see text] subset of it or its complement. This answers a question of Wang. For this, we design a new notion of forcing which generalizes the first and second-jump control of Cholak et al.

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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.