L(R) absoluteness under proper forcings

Ralf Schindler

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arXiv · math/9909043

L(R) absoluteness under proper forcings

Ralf Schindler

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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 "0^sharp-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 Pi^1_1 determinacy.

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BibTeX RIS

Ralf Schindler. 1999-09-08. L(R) absoluteness under proper forcings. https://arxiv.org/abs/math/9909043

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