# Categoricity in abstract elementary classes with no maximal models

@article{VanDieren2005CategoricityIA,
title={Categoricity in abstract elementary classes with no maximal models},
author={Monica M. VanDieren},
journal={Annals of Pure and Applied Logic},
year={2005},
volume={141},
pages={108-147}
}
Limit Models in Classes with Amalgamation
• Mathematics
• 2005
In abstract elementary classes limit models are sometimes the appropriate substitute for saturated models. For Galois-stable abstract elementary classes which satisfy the amalgamation property, we
A survey on tame abstract elementary classes
• Mathematics
• 2015
Tame abstract elementary classes are a broad nonelementary framework for model theory that encompasses several examples of interest. In recent years, progress toward developing a classification
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• S. Vasey
• Mathematics
Selecta Mathematica
• 2019
The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is injective (a
Superstability and symmetry
Superstability and Symmetry
This paper continues the study of superstability in abstract elementary classes (AECs) satisfying the amalgamation property. In particular, we consider the definition of $\mu$-superstability which is
A downward categoricity transfer for tame abstract elementary classes
We prove a downward transfer from categoricity in a successor in tame abstract elementary classes (AECs). This complements the upward transfer of Grossberg and VanDieren and improves the Hanf number
Approximations of superstability in concrete accessible categories
• Mathematics
• 2015
We generalize the constructions and results of Chapter 10 in Baldwin's "Categoricity" to coherent accessible categories with concrete directed colimits and concrete monomorphisms. In particular, we

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