We define a new large cardinal axiom that fits between and in the hierarchy of axioms described in [SRK]. We use this new axiom to obtain a Laver sequence for extendible cardinals, improving the known large cardinal upper bound for the existence of such sequences.
∃κI₃(κ) is the assertion that there is an elementary embedding with critical point below λ, and with λ a limit. The Wholeness Axiom, or WA, asserts that there is a nontrivial elementary embedding j: V → V; WA is formulated in the language ∈,j and has as axioms an Elementarity schema, which asserts that j is elementary; a Critical Point axiom, which asserts that there is a least ordinal moved by j; and includes every instance of the Separation schema for j-formulas. Because no instance of Replacement...
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