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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.

Citation

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Will Boney. "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

Information

Received: 18 September 2013; Accepted: 24 June 2014; Published: 2017
First available in Project Euclid: 25 November 2016

zbMATH: 06686423
MathSciNet: MR3595347
Digital Object Identifier: 10.1215/00294527-3768177

Subjects:
Primary: 03C48
Secondary: 03C45

Rights: Copyright © 2017 University of Notre Dame

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Vol.58 • No. 1 • 2017
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