Journal of Symbolic Logic 68 (4):1317-1336 (2003)
|Abstract||Let K be the class of atomic models of a countable first order theory. We prove that if K is excellent and categorical in some uncountable cardinal, then each model is prime and minimal over the basis of a definable pregeometry given by a quasiminimal set. This implies that K is categorical in all uncountable cardinals. We also introduce a U-rank to measure the complexity of complete types over models. We prove that the U-rank has the usual additivity properties, that quasiminimal types have U-rank 1, and that the U-rank of any type is finite in the uncountably categorical, excellent case. However, in contrast to the first order case, the supremum of the U-rank over all types may be ω (and is not achieved). We illustrate the theory with the example of free groups, and Zilber's pseudo analytic structures|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Anand Pillay (1995). The Geometry of Forking and Groups of Finite Morley Rank. Journal of Symbolic Logic 60 (4):1251-1259.
José Iovino (1996). The Morley Rank of a Banach Space. Journal of Symbolic Logic 61 (3):928-941.
Itay Neeman (2004). The Mitchell Order Below Rank-To-Rank. Journal of Symbolic Logic 69 (4):1143 - 1162.
Frank Wagner (2001). Fields of Finite Morley Rank. Journal of Symbolic Logic 66 (2):703-706.
Olivier Lessmann (2005). Upward Categoricity From a Successor Cardinal for Tame Abstract Classes with Amalgamation. Journal of Symbolic Logic 70 (2):639 - 660.
Ambar Chowdhury & Anand Pillay (1994). On the Number of Models of Uncountable Theories. Journal of Symbolic Logic 59 (4):1285-1300.
Ludomir Newelski (1992). A Model and its Subset. Journal of Symbolic Logic 57 (2):644-658.
David M. Evans & Frank O. Wagner (2000). Supersimple Ω-Categorical Groups and Theories. Journal of Symbolic Logic 65 (2):767-776.
Ronald F. Bustamante Medina (2010). Rank and Dimension in Difference-Differential Fields. Notre Dame Journal of Formal Logic 52 (4):403-414.
Ludomir Newelski (1999). Geometry of *-Finite Types. Journal of Symbolic Logic 64 (4):1375-1395.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Recent downloads (6 months)0
How can I increase my downloads?