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

Annals of Pure and Applied Logic 107 (1-3):227-238 (2001)
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Abstract

Say that the property Φ of a cardinal λ strongly implies the property Ψ. If and only if for every λ,Φ implies that Ψ and that for some λ′<λ,Ψ. 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 j:Lα[Vλ+1]→Lα[Vλ+1] with ”

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10.1016/s0168-0072(00)00035-x

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References found in this work

Elementary embeddings and infinitary combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.
Implications between strong large cardinal axioms.Richard Laver - 1997 - Annals of Pure and Applied Logic 90 (1-3):79-90.
The well-foundedness of the Mitchell order.J. R. Steel - 1993 - Journal of Symbolic Logic 58 (3):931-940.

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