Generalizations of the Kunen inconsistency

Annals of Pure and Applied Logic 163 (12):1872-1890 (2012)

Joel David Hamkins
Oxford University
We present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V to itself. For example, there is no elementary embedding from the universe V to a set-forcing extension V[G], or conversely from V[G] to V, or more generally from one set-forcing ground model of the universe to another, or between any two models that are eventually stationary correct, or from V to HOD, or conversely from HOD to V, or indeed from any definable class to V, among many other possibilities we consider, including generic embeddings, definable embeddings and results not requiring the axiom of choice. We have aimed in this article for a unified presentation that weaves together some previously known unpublished or folklore results, several due to Woodin and others, along with our new contributions
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DOI 10.1016/j.apal.2012.06.001
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References found in this work BETA

Set Theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Elementary Embeddings and Infinitary Combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.
[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.

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Citations of this work BETA

Set-Theoretic Geology.Gunter Fuchs, Joel David Hamkins & Jonas Reitz - 2015 - Annals of Pure and Applied Logic 166 (4):464-501.
The HOD Hypothesis and a Supercompact Cardinal.Yong Cheng - 2017 - Mathematical Logic Quarterly 63 (5):462-472.
The Strong Reflecting Property and Harrington's Principle.Yong Cheng - 2015 - Mathematical Logic Quarterly 61 (4-5):329-340.
Generic Large Cardinals and Systems of Filters.Giorgio Audrito & Silvia Steila - 2017 - Journal of Symbolic Logic 82 (3):860-892.

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