Long reals

David Asperó, Konstantinos Tsaprounis

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3 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalJournal of Logic and Analysis
Issue number1
Publication statusPublished - 1 Oct 2018


  • Real numbers
  • Hessenberg operations
  • Ordered fields
  • Forcing
  • Descriptive set theory

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