Proper forcing and remarkable cardinals II

Journal of Symbolic Logic 66 (3):1481-1492 (2001)
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
Categories (categorize this paper)
DOI 10.2307/2695120
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,392
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Yong Cheng (2015). Forcing a Set Model of Z3 + Harrington's Principle. Mathematical Logic Quarterly 61 (4-5):274-287.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

5 ( #572,778 of 1,924,699 )

Recent downloads (6 months)

1 ( #417,761 of 1,924,699 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.