Homotopy Type Theory Dedekind real unit interval > history (Rev #2, changes)

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Definitions

Large Dedekind real unit interval

The locally 𝒰\mathcal{U}-small Dedekind real unit interval for a universe 𝒰\mathcal{U} is defined as the type of extended $\mathcal{U}$-Dedekind cuts on the open unit interval of the rational numbers (0,1) (0, 1)_\mathbb{Q} in a universe: 𝕀 𝒰ExtendedDedekindCut 𝒰((0,1) )\mathbb{I}_\mathcal{U} \coloneqq ExtendedDedekindCut_\mathcal{U}((0, 1)_\mathbb{Q}).

The 𝒰\mathcal{U}-large Dedekind real numbers for a universe 𝒰\mathcal{U} is defined as the type of extended $\mathcal{U}$-Dedekind cuts on the open unit interval of the rational numbers (0,1) (0, 1)_\mathbb{Q} in a universe: 𝕀 𝒰ExtendedDedekindCut 𝒰((0,1) )\mathbb{I}_\mathcal{U} \coloneqq ExtendedDedekindCut_\mathcal{U}((0, 1)_\mathbb{Q}).

Sigma-Dedekind real unit interval

The Σ\Sigma-Dedekind real numbers for a $\sigma$-frame Σ\Sigma is defined as the type of extended $\Sigma$-Dedekind cuts on the open unit interval of the rational numbers (0,1) (0, 1)_\mathbb{Q}: 𝕀 ΣExtendedDedekindCut Σ((0,1) )\mathbb{I}_\Sigma \coloneqq ExtendedDedekindCut_\Sigma((0, 1)_\mathbb{Q}).

See also

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