We show that the number of types of sequences of tuples of a fixed length can be calculated from the number of -types and the length of the sequences. Specifically, if , then
We show that this holds for any abstract elementary class with -amalgamation. No such calculation is possible for nonalgebraic types. However, we introduce a subclass of nonalgebraic types for which the same upper bound holds.
"Computing the Number of Types of Infinite Length." Notre Dame J. Formal Logic 58 (1) 133 - 154, 2017. https://doi.org/10.1215/00294527-3768177