OAI/Analysis/PureInfiniteness/AbsorptionFromCentralCopy.lean

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Absorption from a central embedding and a connected approximate half-flip, using the nuclearity and simplicity of O∞ and Kirchberg's criterion.

  1. theorem OAI.WeakPureInfiniteness.Campaign.nuclear_absorption_from_central_embedding_and_halfFlip line 25

    Source documentation

    The full absorption corollary, still conditional on the published central embedding and connected half-flip; O∞ nuclearity and simplicity are proved.

    theorem nuclear_absorption_from_central_embedding_and_halfFlip
        (U : Ultrafilter ℕ) [Fact ((U : Filter ℕ) ≤ atTop)]
        (hcentral : Nontrivial A → Nuclear A → StronglyPurelyInfinite A →
          Nonempty (OInfinity →⋆ₐ[ℂ]
            NonunitalGamma.CentralSequenceAlgebra (A := A) U))
    …

    Mentions: OAI.WeakPureInfiniteness.Nuclear, OAI.WeakPureInfiniteness.StronglyPurelyInfinite, OAI.WeakPureInfiniteness.OInfinity, OAI.NonunitalGamma.CentralSequenceAlgebra