Journal of Symbolic Logic 66 (3):1090-1116 (2001)

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Abstract
We consider the following question of Kunen: Does Con(ZFC + ∃M a transitive inner model and a non-trivial elementary embedding j: M $\longrightarrow$ V) imply Con (ZFC + ∃ a measurable cardinal)? We use core model theory to investigate consequences of the existence of such a j: M → V. We prove, amongst other things, the existence of such an embedding implies that the core model K is a model of "there exists a proper class of almost Ramsey cardinals". Conversely, if On is Ramsey, then such a j, M are definable. We construe this as a negative answer to the question above. We consider further the consequences of strengthening the closure assumption on j to having various classes of fixed points
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DOI 10.2307/2695094
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References found in this work BETA

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
Countable Unions of Simple Sets in the Core Model.P. D. Welch - 1996 - Journal of Symbolic Logic 61 (1):293-312.

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Citations of this work BETA

Plural Quantification and Classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.
Generalizations of the Kunen Inconsistency.Joel David Hamkins, Greg Kirmayer & Norman Lewis Perlmutter - 2012 - Annals of Pure and Applied Logic 163 (12):1872-1890.
Making All Cardinals Almost Ramsey.Arthur W. Apter & Peter Koepke - 2008 - Archive for Mathematical Logic 47 (7-8):769-783.

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