Computing the number of types of infinite length
Will Boney · 2013
We show that the number of types of sequences of tuples of a fixed length can be calculated from the number of 1-types and the length of the sequences. Specifically, if κ ≤ λ, then sup |S |A|=λ κ (A) | = sup |S |A|=λ 1 (A)| We show that this holds for any abstract elementary class with λ amalgamation, but it is new for first order theories when κ is infinite. No such calculation is possible for nonalgebraic types. We introduce a generalization of nonalgebraic