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Real numbers and other completions

✍ Scribed by Fred Richman

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
135 KB
Volume
54
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete Archimedean Heyting field, a terminal object in the category of Archimedean Heyting fields. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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## Abstract In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure – Dedekind‐complete ordered field. Even the effective versions of these representations are equivalent in