Consistency of V = HOD with the wholeness axiom

Archive for Mathematical Logic 39 (3):219-226 (2000)
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Abstract

The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language $\{\in,j\}$ , and that asserts the existence of a nontrivial elementary embedding $j:V\to V$ . The well-known inconsistency proofs are avoided by omitting from the schema all instances of Replacement for j-formulas. We show that the theory ZFC + V = HOD + WA is consistent relative to the existence of an $I_1$ embedding. This answers a question about the existence of Laver sequences for regular classes of set embeddings: Assuming there is an $I_1$ -embedding, there is a transitive model of ZFC +WA + “there is a regular class of embeddings that admits no Laver sequence.”

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Citations of this work

The wholeness axiom and Laver sequences.Paul Corazza - 2000 - Annals of Pure and Applied Logic 105 (1-3):157-260.
The spectrum of elementary embeddings j: V→ V.Paul Corazza - 2006 - Annals of Pure and Applied Logic 139 (1):327-399.
The Axiom of Infinity and Transformations j: V → V.Paul Corazza - 2010 - Bulletin of Symbolic Logic 16 (1):37-84.
Lifting elementary embeddings j: V λ → V λ. [REVIEW]Paul Corazza - 2007 - Archive for Mathematical Logic 46 (2):61-72.

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