Graduate studies at Western
Journal of Symbolic Logic 62 (2):438-456 (1997)
|Abstract||Let DO denote the principle: Every infinite set has a dense linear ordering. DO is compared to other ordering principles such as O, the Linear Ordering principle, KW, the Kinna-Wagner Principle, and PI, the Prime Ideal Theorem, in ZF, Zermelo-Fraenkel set theory without AC, the Axiom of Choice. The main result is: Theorem. $AC \Longrightarrow KW \Longrightarrow DO \Longrightarrow O$ , and none of the implications is reversible in ZF + PI. The first and third implications and their irreversibilities were known. The middle one is new. Along the way other results of interest are established. O, while not quite implying DO, does imply that every set differs finitely from a densely ordered set. The independence result for ZF is reduced to one for Fraenkel-Mostowski models by showing that DO falls into two of the known classes of statements automatically transferable from Fraenkel-Mostowski to ZF models. Finally, the proof of PI in the Fraenkel-Mostowski model leads naturally to versions of the Ramsey and Ehrenfeucht-Mostowski theorems involving sets that are both ordered and colored|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
William C. Calhoun (2006). Degrees of Monotone Complexity. Journal of Symbolic Logic 71 (4):1327 - 1341.
Laura Crosilla, Hajime Ishihara & Peter Schuster (2005). On Constructing Completions. Journal of Symbolic Logic 70 (3):969-978.
Juha Oikkonen (1990). On Ehrenfeucht-Fraïssé Equivalence of Linear Orderings. Journal of Symbolic Logic 55 (1):65-73.
C. J. Ash (1991). A Construction for Recursive Linear Orderings. Journal of Symbolic Logic 56 (2):673-683.
Masaru Shirahata (1996). A Linear Conservative Extension of Zermelo-Fraenkel Set Theory. Studia Logica 56 (3):361 - 392.
Antonio Montalbán (2005). Up to Equimorphism, Hyperarithmetic Is Recursive. Journal of Symbolic Logic 70 (2):360 - 378.
Paul E. Howard (1973). Limitations on the Fraenkel-Mostowski Method of Independence Proofs. Journal of Symbolic Logic 38 (3):416-422.
U. Felgner & J. K. Truss (1999). The Independence of the Prime Ideal Theorem From the Order-Extension Principle. Journal of Symbolic Logic 64 (1):199-215.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #294,156 of 751,836 )
Recent downloads (6 months)0
How can I increase my downloads?