Journal of Mathematical Logic 10 (1):101-339 (2010)

W. Hugh Woodin
Harvard University
We investigate both iteration hypotheses and extender models at the level of one supercompact cardinal. The HOD Conjecture is introduced and shown to be a key conjecture both for the Inner Model Program and for understanding the limits of the large cardinal hierarchy. We show that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Gödel's constructible universe L. Whether or not this "ultimate" L exists is now arguably the central issue for the Inner Model Program.
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DOI 10.1142/S021906131000095X
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References found in this work BETA

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Descriptive Set Theory.Richard Mansfield - 1981 - Journal of Symbolic Logic 46 (4):874-876.
Inner Models in the Region of a Woodin Limit of Woodin Cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
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

Large Cardinals Beyond Choice.Joan Bagaria, Peter Koellner & W. Hugh Woodin - 2019 - Bulletin of Symbolic Logic 25 (3):283-318.
Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.
Suitable Extender Models II: Beyond Ω-Huge.W. Hugh Woodin - 2011 - Journal of Mathematical Logic 11 (2):115-436.
The Long Extender Algebra.Ralf Schindler - 2018 - Archive for Mathematical Logic 57 (1-2):73-82.

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