The mouse set conjecture for sets of reals

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Journal of Symbolic Logic 80 (2):671-683 (2015)
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10.1017/jsl.2014.78

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Review: Donald A. Martin, John R. Steel, Projective Determinacy; W. Hugh Woodin, Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees; Donald A. Martin, John R. Steel, A Proof of Projective Determinacy. [REVIEW]Matthew D. Foreman - 1992 - Journal of Symbolic Logic 57 (3):1132-1136.
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J. Steel, PFA implies_ AD _L_(ℝ). _ _The Journal of Symbolic Logic_ _, vol. 70 (2005), no. 4, pp. 1255–1296. - G. Sargsyan, _Nontame mouse from the failure of square at a singular strong limit cardinal_. _ _Journal of Mathematical Logic_ _, vol. 14 (2014), 1450003 (47 pages). - G. Sargsyan, _Covering with universally Baire operators_. _ _Advances in Mathematics_ _, vol. 268 (2015), pp. 603–665. - N. Trang, _PFA and guessing models_. _ _Israel Journal of Mathematics_ , vol. 215 (2016), pp. 607–667. [REVIEW]Sandra Müller - 2020 - Bulletin of Symbolic Logic 26 (1):89-92.
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Donald A. Martin and John R. Steel. Projective determinacy. Proceedings of the National Academy of Sciences of the United States of America, vol. 85 , pp. 6582–6586. - W. Hugh Woodin. Supercompact cardinals, sets of reals, and weakly homogeneous trees. Proceedings of the National Academy of Sciences of the United States of America, vol. 85 , pp. 6587–6591. - Donald A. Martin and John R. Steel. A proof of projective determinacy. Journal of the American Mathematical Society, vol. 2 , pp. 71–125. [REVIEW]Matthew D. Foreman - 1992 - Journal of Symbolic Logic 57 (3):1132-1136.
From a well-ordering of the reals it is easy (by a diagonal argument) to produce a non-determined set of reals. However, large cardinal axioms imply that all sets of reals in L (R), and more, are determined. See, for example, Neeman's papers Optimalproofs of determinacy.Andrzej S. Murawski - 1995 - Bulletin of Symbolic Logic 1:327-339.
-Sets of reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72-80.
-Sets of reals.Jaime I. Ihoda - 1988 - Journal of Symbolic Logic 53 (2):636-642.
Sets of reals.Joan Bagaria & W. Hugh Woodin - 1997 - Journal of Symbolic Logic 62 (4):1379-1428.

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Jack Steel
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Citations of this work

Realizing an AD + model as a derived model of a premouse.Yizheng Zhu - 2015 - Annals of Pure and Applied Logic 166 (12):1275-1364.
Determinacy from strong compactness of ω1.Nam Trang & Trevor M. Wilson - 2021 - Annals of Pure and Applied Logic 172 (6):102944.

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