Long reals

Asperó, David and Tsaprounis, Konstantinos (2018) Long reals. Journal of Logic and Analysis, 10 (1). pp. 1-36. ISSN 1759-9008

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Abstract

The familiar continuum R of real numbers is obtained by a well-known procedure which, starting with the set of natural numbers N=\omega, produces in a canonical fashion the field of rationals Q and, then, the field R as the completion of Q under Cauchy sequences (or, equivalently, using Dedekind cuts). In this article, we replace \omega by any infinite suitably closed ordinal \kappa in the above construction and, using the natural (Hessenberg) ordinal operations, we obtain the corresponding field \kappa-R, which we call the field of the \kappa-reals. Subsequently, we study the properties of the various fields \kappa-R and develop their general theory, mainly from the set-theoretic perspective. For example, we investigate their connection with standard themes such as forcing and descriptive set theory.

Item Type: Article
Uncontrolled Keywords: real numbers,hessenberg operations,ordered fields,forcing,descriptive set theory
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 06 Feb 2018 10:31
Last Modified: 15 Nov 2020 00:54
URI: https://ueaeprints.uea.ac.uk/id/eprint/66229
DOI: 10.4115/jla.2018.10.1

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