The axiom of reflection
The dependence of some logical axioms on disjoint transversals and linked systems
The gap between I₃ and the wholeness axiom
∃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...
The Wholeness Axioms and the Class of Supercompact Cardinals
We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.
Trees, inverse systems, and valuated vector spaces