72 + 42: CHARACTERIZATIONS OF THE COMPLETENESS AND ARCHIMEDEAN PROPERTIES OF ORDERED FIELDS

Michael Deveau; Holger Teismann

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72 + 42: CHARACTERIZATIONS OF THE COMPLETENESS AND ARCHIMEDEAN PROPERTIES OF ORDERED FIELDS

机译：72 + 42：有序场的完备性和Archimedean性质

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This paper provides a list of statements of single-variable Real Analysis, including well-known theorems, that are equivalent to the completeness or Archimedean properties of totally ordered fields. There are 72 characterizations of completeness and 42 characterizations of the Archimedean property, among them many that appear to be new in the sense that they do not seem to have previously been mentioned in this context. An attempt is made to be as comprehensive as possible and to give a complete account of the current state of knowledge of the matter. Proofs are provided whenever they are not readily available in the literature.

机译：本文提供了单变量实数分析的语句列表，包括众所周知的定理，这些定理等同于完全有序字段的完整性或Archimedean属性。有72个完整性的特征和42个Archimedean属性的特征，其中许多似乎是新的，因为它们在此之前似乎并未被提及。力求尽可能全面，并全面说明该问题的当前知识状态。只要文献中不易提供，就提供证明。

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来源
《Real analysis exchange》 |2014年第2期|261-303|共43页
作者
Michael Deveau; Holger Teismann;
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作者单位

Pure Mathematics, University of Waterloo, Waterloo, ON Canada N2L 3G1;

Department of Mathematics, Acadia University, Wolfville, NS Canada B4P 2R6;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Ordered field; completeness; Archimedean Property; single variable analysis;

机译：有序字段;完整性阿基米德财产;单变量分析;

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72 + 42: CHARACTERIZATIONS OF THE COMPLETENESS AND ARCHIMEDEAN PROPERTIES OF ORDERED FIELDS

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