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Proper forcing and remarkable cardinals II

Published online by Cambridge University Press:  12 March 2014

Ralf-Dieter Schindler
Ralf-Dieter Schindler*
Affiliation:
Institut für Formale Logik, Universität Wien, 1090 Wien, Austria, E-mail: rds@logic.univie.ae.at, URL: http://www.logic.univie.ac.at/~rds/
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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-Erdös cardinals. They are characterized by the existence of “0#-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 determinacy.

Keywords

set theory/descriptive set theory/proper forcing/large cardinals
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1481 - 1492
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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