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A new large cardinal and Laver sequences for extendibles

Paul Corazza — 1997

Fundamenta Mathematicae

We define a new large cardinal axiom that fits between $A_{3}$ and $A_{4}$ 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.

The gap between I₃ and the wholeness axiom

Paul Corazza — 2003

Fundamenta Mathematicae

∃κI₃(κ) is the assertion that there is an elementary embedding $i : V_{λ} \to V_{λ}$ 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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