L(R) absoluteness under proper forcings
Abstract
We isolate a new large cardinal concept, "remarkability." Consistencywise, remarkable cardinals are between ineffable and omega-Erdos cardinals. They are characterized by the existence of "0sharp-like" embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L(R) absoluteness under proper forcings. In particular, said absoluteness does not imply Pi11 determinacy.
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