## 50 Citations

Categoricity in abstract elementary classes with no maximal models

- MathematicsAnn. Pure Appl. Log.
- 2006

Superstability from categoricity in abstract elementary classes

- MathematicsAnn. Pure Appl. Log.
- 2017

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…

Uncountable categoricity of local abstract elementary classes with amalgamation

- MathematicsAnn. Pure Appl. Log.
- 2006

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…

The categoricity spectrum of large abstract elementary classes

- MathematicsSelecta 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

- Mathematics
- 2015

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

- Mathematics
- 2015

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…

## References

SHOWING 1-10 OF 28 REFERENCES

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…

Categoricity of an abstract elementary class in two successive cardinals

- Mathematics
- 1998

We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models, or existence of large cardinals). We…

Ehrenfeucht-Mostowski models in Abstract Elementary Classes

- Mathematics
- 2003

In [15], Shelah proclaims the aim of reconstructing model theory, ‘with no use of even traces compactness’. We analyze here one aspect of this program. Keisler organizes [8] around four kinds of…

Categoricity in abstract elementary classes: going up inductive step

- Mathematics
- 2000

We deal with stability theory for ``reasonable'' non-elementary classes without any remanents of compactness (like: above Hanf number or definable by L_{omega_1, omega}).

Classification theory - and the number of non-isomorphic models, Second Edition

- MathematicsStudies in logic and the foundations of mathematics
- 1990

Upward Stability Transfer for Tame Abstract Elementary Classes

- MathematicsNotre Dame J. Formal Log.
- 2006

This work names some variants of tameness and proves the following, which is a very strong conclusion in the countable case: K is Galois-stable in all cardinalities.

Abstract Classes with Few Models Have 'Homogeneous-Universal' Models

- MathematicsJ. Symb. Log.
- 1995

It is shown that closure can be replaced by the existence of a bound for each chain and even stronger that the authors need the boundedness only for a 'dense' (in a sense made precise by a game defined below) set of chains.

Classification theory for non-elementary classes I: The number of uncountable models of
$$\psi \in L_{w_1 ,w} $$
. Part B. Part B

- Mathematics
- 1983

We continue here Part A, and the main results are proved here. This part deals withn-dimensional diagrams of models.