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A Candidate for the Generalised Real Line

  • Lorenzo Galeotti
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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