Open Access
2017 Computing the Number of Types of Infinite Length
Will Boney
Notre Dame J. Formal Logic 58(1): 133-154 (2017). DOI: 10.1215/00294527-3768177
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 κλ, then

sup M=λ|Sκ(M)|=(sup M=λ|S1(M)|)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.

Copyright © 2017 University of Notre Dame
Will Boney "Computing the Number of Types of Infinite Length," Notre Dame Journal of Formal Logic 58(1), 133-154, (2017). https://doi.org/10.1215/00294527-3768177
Received: 18 September 2013; Accepted: 24 June 2014; Published: 2017
Vol.58 • No. 1 • 2017
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