A Candidate for the Generalised Real Line

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9709)

Abstract

Let \(\kappa \) be an uncountable cardinal with \(\kappa ^{<\kappa }=\kappa \). In this paper we introduce \({{\mathrm{\mathbb {R}}}}_\kappa \), a Cauchy-complete real closed field of cardinality \(2^\kappa \). We will prove that \({{\mathrm{\mathbb {R}}}}_\kappa \) shares many features with \({{\mathrm{\mathbb {R}}}}\) which have a key role in real analysis and computable analysis. In particular, we will prove that the Intermediate Value Theorem holds for a non-trivial subclass of continuous functions over \({{\mathrm{\mathbb {R}}}}_\kappa \). We propose \({{\mathrm{\mathbb {R}}}}_\kappa \) as a candidate for extending computable analysis to generalised Baire spaces.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Universität HamburgHamburgGermany

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