Journal of Symbolic Logic 60 (1):160-171 (1995)
| Abstract |
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 |
| Options |
Mark as duplicate
Export citation
Request removal from index
|
Download options
PhilArchive copy
Upload a copy of this paper Check publisher's policy Papers currently archived: 70,265
External links
- From the Publisher via CrossRef (no proxy)
- projecteuclid.org
(no proxy) - projecteuclid.org [2] (no proxy)
- projecteuclid.org [3] (no proxy)
- journals.cambridge.org (no proxy)
- jstor.org (no proxy)
- jstor.org [2] (no proxy)
- jstor.org [3] (no proxy)
- cambridge.org (no proxy)
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
- Sign in / register and customize your OpenURL resolver..
- Configure custom resolver
References found in this work BETA
Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
The Theory of Boolean Ultrapowers.Richard Mansfield - 1971 - Annals of Mathematical Logic 2 (3):297-323.
Remarks on the Nonstandard Real Axis.Elias Zakon - 1969 - In W. A. J. Luxemburg (ed.), Applications of Model Theory to Algebra, Analysis, and Probability. New York: Holt, Rinehart and Winston. pp. 195--227.
View all 6 references / Add more references
Citations of this work BETA
Background Independence in Quantum Gravity and Forcing Constructions.Jerzy Król - 2004 - Foundations of Physics 34 (3):361-403.
Quantum Set Theory: Transfer Principle and De Morgan's Laws.Masanao Ozawa - 2021 - Annals of Pure and Applied Logic 172 (4):102938.
The Trend of Logic and Foundation of Mathematics in Japan in 1991 to 1996.Yuzuru Kakuda, Kanji Namba & Nobuyoshi Motohashi - 1997 - Annals of the Japan Association for Philosophy of Science 9 (2):95-110.
Similar books and articles
On Dedekind Complete o-Minimal Structures.Anand Pillay & Charles Steinhorn - 1987 - Journal of Symbolic Logic 52 (1):156-164.
Zorn's Lemma and Complete Boolean Algebras in Intuitionistic Type Theories.J. L. Bell - 1997 - Journal of Symbolic Logic 62 (4):1265-1279.
Regular Subalgebras of Complete Boolean Algebras.Aleksander Błaszczyk & Saharon Shelah - 2001 - Journal of Symbolic Logic 66 (2):792-800.
On Countably Closed Complete Boolean Algebras.Thomas Jech & Saharon Shelah - 1996 - Journal of Symbolic Logic 61 (4):1380-1386.
Elementary Embedding Between Countable Boolean Algebras.Robert Bonnet & Matatyahu Rubin - 1991 - Journal of Symbolic Logic 56 (4):1212-1229.
Boolean Universes Above Boolean Models.Friedrich Wehrung - 1993 - Journal of Symbolic Logic 58 (4):1219-1250.
Definable Sets in Boolean-Ordered o-Minimal Structures. I.Ludomir Newelski & Roman Wencel - 2001 - Journal of Symbolic Logic 66 (4):1821-1836.
The Modal Logic of Continuous Functions on the Rational Numbers.Philip Kremer - 2010 - Archive for Mathematical Logic 49 (4):519-527.
Analytics
Added to PP index
2009-01-28
Total views
53 ( #214,236 of 2,507,664 )
Recent downloads (6 months)
1 ( #416,871 of 2,507,664 )
2009-01-28
Total views
53 ( #214,236 of 2,507,664 )
Recent downloads (6 months)
1 ( #416,871 of 2,507,664 )
How can I increase my downloads?
Downloads
