Square in core models

Bulletin of Symbolic Logic 7 (3):305-314 (2001)
We prove that in all Mitchell-Steel core models, □ κ holds for all κ. (See Theorem 2.). From this we obtain new consistency strength lower bounds for the failure of □ κ if κ is either singular and countably closed, weakly compact, or measurable. (Corallaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ κ holds iff κ is not subcompact. (See Theorem 15; the only if direction is essentially due to Jensen.)
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2687750
 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: 20,465
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
Martin Zeman (2010). Global Square Sequences in Extender Models. Annals of Pure and Applied Logic 161 (7):956-985.
Jason Aaron Schanker (2013). Partial Near Supercompactness. Annals of Pure and Applied Logic 164 (2):67-85.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

10 ( #332,219 of 1,796,529 )

Recent downloads (6 months)

1 ( #466,501 of 1,796,529 )

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.