Journal of Symbolic Logic 66 (3):1481-1492 (2001)

Abstract
The current paper proves the results announced in [5]. We isolate a new large cardinal concept, "remarkability." Consistencywise, remarkable cardinals are between ineffable and ω-Erdos cardinals. They are characterized by the existence of "O # -like" embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L(R) absoluteness for proper forcings. In particular, said absoluteness does not imply Π 1 1 determinacy
Keywords Set Theory   Descriptive Set Theory   Proper Forcing   Large Cardinals
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DOI 10.2307/2695120
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References found in this work BETA

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
Proper Forcing and Remarkable Cardinals.Ralf-Dieter Schindler - 2000 - Bulletin of Symbolic Logic 6 (2):176-184.

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Citations of this work BETA

Forcing and the Universe of Sets: Must We Lose Insight?Neil Barton - 2020 - Journal of Philosophical Logic 49 (4):575-612.
Absoluteness Via Resurrection.Giorgio Audrito & Matteo Viale - 2017 - Journal of Mathematical Logic 17 (2):1750005.

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