Lifting elementary embeddings j: Vλ → Vλ

Archive for Mathematical Logic 46 (2):61-72 (2007)
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Abstract

We describe a fairly general procedure for preserving I3 embeddings j: Vλ → Vλ via λ-stage reverse Easton iterated forcings. We use this method to prove that, assuming the consistency of an I3 embedding, V = HOD is consistent with the theory ZFC + WA where WA is an axiom schema in the language {∈, j} asserting a strong but not inconsistent form of “there is an elementary embedding V → V”. This improves upon an earlier result in which consistency was established assuming an I1 embedding.

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References found in this work

Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
Laver sequences for extendible and super-almost-huge cardinals.Paul Corazza - 1999 - Journal of Symbolic Logic 64 (3):963-983.
The Wholeness Axioms and V=HOD.Joel David Hamkins - 2001 - Archive for Mathematical Logic 40 (1):1-8.
Iterating ordinal definability.Wlodzimierz Zadrozny - 1983 - Annals of Mathematical Logic 24 (3):263-310.

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