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

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

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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DOI 10.1016/s0168-0072(00)00035-x
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References found in this work BETA

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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Citations of this work BETA

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A Partially Non-Proper Ordinal Beyond L.Vincenzo Dimonte - 2012 - Annals of Pure and Applied Logic 163 (9):1309-1321.
$$I_0$$ I 0 and Combinatorics at $$\Lambda ^+$$ Λ +.Shi Xianghui & Trang Nam - 2017 - Archive for Mathematical Logic 56 (1-2):131-154.

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