On elementary embeddings from an inner model to the universe

Journal of Symbolic Logic 66 (3):1090-1116 (2001)
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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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References found in this work

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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