Journal of Symbolic Logic 64 (1):199-215 (1999)
|Abstract||It is shown that the boolean prime ideal theorem BPIT: every boolean algebra has a prime ideal, does not follow from the order-extension principle OE: every partial ordering can be extended to a linear ordering. The proof uses a Fraenkel-Mostowski model, where the family of atoms is indexed by a countable universal-homogeneous boolean algebra whose boolean partial ordering has a `generic' extension to a linear ordering. To illustrate the technique for proving that the order-extension principle holds in the model we also study Mostowski's ordered model, and give a direct verification of OE there. The key technical point needed to verify OE in each case is the existence of a support structure|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Paul Studtmann (2006). Prime Matter and Extension in Aristotle. Journal of Philosophical Research 31:171-184.
Mohamed A. Amer (1985). Extension of Relatively |Sigma-Additive Probabilities on Boolean Algebras of Logic. Journal of Symbolic Logic 50 (3):589 - 596.
Peter Milne (2004). Algebras of Intervals and a Logic of Conditional Assertions. Journal of Philosophical Logic 33 (5):497-548.
E. W. Madison (1983). The Existence of Countable Totally Nonconstructive Extensions of the Countable Atomless Boolean Algebra. Journal of Symbolic Logic 48 (1):167-170.
John Bell (2003). Some New Intuitionistic Equivalents of Zorn's Lemma. Archive for Mathematical Logic 42 (8):811-814.
Paul E. Howard (1973). Limitations on the Fraenkel-Mostowski Method of Independence Proofs. Journal of Symbolic Logic 38 (3):416-422.
Robert Bonnet & Matatyahu Rubin (1991). Elementary Embedding Between Countable Boolean Algebras. Journal of Symbolic Logic 56 (4):1212-1229.
David Pincus (1997). The Dense Linear Ordering Principle. Journal of Symbolic Logic 62 (2):438-456.
Menachem Kojman & Saharon Shelah (1992). Nonexistence of Universal Orders in Many Cardinals. Journal of Symbolic Logic 57 (3):875-891.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #291,125 of 722,745 )
Recent downloads (6 months)1 ( #60,247 of 722,745 )
How can I increase my downloads?