Reflection of elementary embedding axioms on the L[Vλ+1] hierarchy Original Research Article

Say that the property Φ(λ) of a cardinal λ strongly implies the property Ψ(λ). If and only if for every λ,Φ(λ) implies that Ψ(λ) and that for some λ′<λ,Ψ(λ′). Frequently in the hierarchy of large cardinal axioms, stronger axioms strongly imply weaker ones. Some strong implications are proved between axioms of the form “there is an elementary embedding View the MathML source with View the MathML source”.