Consistency of V = HOD with the wholeness axiom

The Wholeness Axiom (WA) is an axiom schema that can be added to the axioms of ZFC in an extended language {, j}, and that asserts the existence of a nontrivial elementary embedding j : V 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 I1 embedding. This answers a question about the existence of Laver sequences for regular classes of set embeddings: Assuming there is an I1-embedding, there is a transitive model of ZFC+WA+ "there is a regular class of embeddings that admits no Laver sequence." 1991 Mathematics Subject Classification. Primary 03E55, 03E35. Keywords and phrases. Wholeness Axiom, elementary embeddings, HOD, regular classes, Laver sequences. 1 

• Type: Journal
• Year: 2000
• Where: AML
• Authors: Paul Corazza
• Keywords: AML 2000, Laver Sequences, Nontrivial Elementary Embedding, Wholeness Axiom