L(R) absoluteness under proper forcings
Logic
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/9909043,
title = {L(R) absoluteness under proper forcings},
author = {Ralf Schindler},
journal= {arXiv preprint arXiv:math/9909043},
year = {2007}
}
Comments
15 pages