理查德·戴德金的传奇命运

IF 0.6 Q3 MULTIDISCIPLINARY SCIENCES

Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali Pub Date : 2021-09-30 DOI:10.1478/AAPP.99S1A18

G. Devillanova, Giovanni Molica Bisci

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引用次数: 2

摘要

通过使用前面的注释中给出的初步结果，我们在这里简要而自我包含地介绍了实域作为唯一的，直到增加同构的，Dedekind完全全序域的构造。此外，我们还证明了全序域上的Dedekind完备性与文献中一些有意义的众所周知的概念之间的等价性，例如全序阿基米德域上的Cauchy完备性。这个表征结果使我们能够在度量空间的一般抽象设置中正确地编码全序域的Dedekind完备性。我们相信，任何有抽象数学思维经验的人都可以很容易地阅读论文的重要部分。本文完成了第二作者于2018年6月在墨西拿举行的科学教学新视野国际研讨会上的演讲。

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 fabulous destiny of Richard Dedekind

By using the preliminary results given in a previous divulgative note, we present here a concise and self–contained introduction to the construction of the real field as the unique, up to increasing isomorphism, Dedekind complete totally ordered field. Moreover, we also show the equivalence between the Dedekind completeness property on totally ordered fields and some meaningful well–known notions present in the literature, such as the Cauchy completeness on totally ordered Archimedean fields. This characterization result allows us to correctly encode the Dedekind completeness for totally ordered fields in the general abstract setting of metric spaces. We believe that the essential parts of the paper can be easily accessed by anyone with some experience in abstract mathematical thinking. The paper completes the lecture given by the second author during the International Workshop on New Horizons in Teaching Science in Messina on June 2018.

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来源期刊

Atti Accademia Peloritana dei Pericolanti-Classe di Scienze Fisiche Matematiche e Naturali MULTIDISCIPLINARY SCIENCES-

CiteScore

3.80

自引率

0.00%

发文量

审稿时长

31 weeks

期刊介绍： This journal is of a multi- and inter-disciplinary nature and covers a broad range of fields including mathematics, computer science, physics, chemistry, biology, earth sciences, and their intersection. History of science is also included within the topics addressed by the journal. The transactions of the Pelorian Academy started out as periodic news sheets containing the notes presented by the members of the Divisions into which the Academy has been and still is organized, according to subject areas. The publication of these notes for the Division (“Classe”) of Mathematical, Physical and Natural Sciences is the responsibility of the Editorial Committee, which is composed of the Director of the division with the role of Chairman, the Vice-Director, the Secretary and two or more other members. Besides original research articles, the journal also accepts texts from conferences and invited talks held in the Academy. These contributions are published in a different section of the journal. In addition to the regular issues, single monographic supplements are occasionally published which assemble reports and communications presented at congresses, symposia, seminars, study meetings and other scientific events organized by the Academy or under its patronage. Since 2004 these transactions have been published online in the form of an open access electronic journal.