Homotopy Type Theory Dedekind complete Archimedean ordered integral domain > history (Rev #4, changes)

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Defintion

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Archimedean ordered integral domain FF is Dedekind complete if

  • For all terms a:Fa:F and b:Fb:F, the open interval (a,b)(a,b) is inhabited.

  • For all terms a:Fa:F, the lower bounded open interval (a,)(a,\infty) is inhabited.

  • For all terms a:Fa:F, the upper bounded open interval (,a)(-\infty,a) is inhabited.

  • For all terms a:Fa:F and b:Fb:F, a<ba \lt b if and only if (b,)(b,\infty) is a subinterval of (a,)(a,\infty)

  • For all terms a:Fa:F and b:Fb:F, b<ab \lt a if and only if (,b)(-\infty,b) is a subinterval of (,a)(-\infty,a)

  • For all terms a:Fa:F and b:Fb:F, if a<ba \lt b, then FF is a subinterval of the union of (a,)(a, \infty) and (,b)(-\infty, b)

  • For all terms a:Fa:F and b:Fb:F, the intersection of (a,)(a,\infty) and (,b)(-\infty,b) is a subinterval of (a,b)(a,b)

See also

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