在图灵等价下闭合的实数集：域、阶和自同构的应用

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2023-02-16 DOI:10.1007/s00153-023-00865-7

Iván Ongay-Valverde

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引用次数: 0

摘要

在本文的前半部分，我们从代数、测度和阶的角度研究了图灵等价下封闭的实数集合位于实数线内的方式。然后，我们将这些集作为阶的研究结果与亚伯拉罕的一个经典构造结合起来，得到了图灵度的非平凡自同构(如果存在的话)如何与1-泛型度相互作用的限制。

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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Sets of real numbers closed under Turing equivalence: applications to fields, orders and automorphisms

In the first half of this paper, we study the way that sets of real numbers closed under Turing equivalence sit inside the real line from the perspective of algebra, measure and orders. Afterwards, we combine the results from our study of these sets as orders with a classical construction from Avraham to obtain a restriction about how non trivial automorphism of the Turing degrees (if they exist) interact with 1-generic degrees.

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

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.