Computing the Number of Types of Infinite Length

Notre Dame Journal of Formal Logic 58 (1):133-154 (2017)
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Abstract

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 ‖M‖=λ|Sκ|=|)κ. We show that this holds for any abstract elementary class with λ-amalgamation. No such calculation is possible for nonalgebraic types. However, we introduce a subclass of nonalgebraic types for which the same upper bound holds.

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10.1215/00294527-3768177

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References found in this work

Model theory for infinitary logic.H. Jerome Keisler - 1971 - Amsterdam,: North-Holland Pub. Co..
[Introduction].Wilfrid Hodges - 1988 - Journal of Symbolic Logic 53 (1):1.
Galois-stability for Tame abstract elementary classes.Rami Grossberg & Monica Vandieren - 2006 - Journal of Mathematical Logic 6 (01):25-48.

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