Constructing the Reals as Dedekind Cuts of Rationals

Jacques D. Fleuriot and Lawrence C. Paulson

March 24, 2022

Abstract

The type of real numbers is constructed from the positive rationals using the method of Dedekind cuts. This development, briefly described in papers by the authors, follows the textbook presentation by Gleason. It's notable that the first formalisation of a significant piece of mathematics, by Jutting in 1977, involved a similar construction.
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Theories of Dedekind_Real

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@article{Dedekind_Real-AFP,
  author  = {Jacques D. Fleuriot and Lawrence C. Paulson},
  title   = {Constructing the Reals as Dedekind Cuts of Rationals},
  journal = {Archive of Formal Proofs},
  month   = {March},
  year    = {2022},
  note    = {\url{https://isa-afp.org/entries/Dedekind_Real.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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