Scott incomplete Boolean ultrapowers of the real line

Journal of Symbolic Logic 60 (1):160-171 (1995)
An ordered field is said to be Scott complete iff it is complete with respect to its uniform structure. Zakon has asked whether nonstandard real lines are Scott complete. We prove in ZFC that for any complete Boolean algebra B which is not (ω, 2)-distributive there is an ultrafilter U of B such that the Boolean ultrapower of the real line modulo U is not Scott complete. We also show how forcing in set theory gives rise to examples of Boolean ultrapowers of the real line which are not Scott complete
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275513
 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: 23,316
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
Richard Mansfield (1971). The Theory of Boolean Ultrapowers. Annals of Mathematical Logic 2 (3):297-323.
Masanao Ozawa (1994). Forcing in Nonstandard Analysis. Annals of Pure and Applied Logic 68 (3):263-297.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

11 ( #382,597 of 1,932,585 )

Recent downloads (6 months)

1 ( #456,398 of 1,932,585 )

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.