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}
}
View PDF on arXiv
50 Citations
Highly Influential Citations
4
Background Citations
7
Methods Citations
4
Results Citations
1

50 Citations

Citation Type

Citation Type

Categoricity in abstract elementary classes with no maximal models
Superstability from categoricity in abstract elementary classes
Limit Models in Classes with Amalgamation
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
A survey on tame abstract elementary classes
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
  • 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
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…
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 28 REFERENCES
Toward Categoricity for Classes with no Maximal Models
Limit Models in Classes with Amalgamation
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
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…
Categoricity for Abstract Classes with Amalgamation
  • S. Shelah
  • Mathematics
    Ann. Pure Appl. Log.
  • 1999
Ehrenfeucht-Mostowski models in Abstract Elementary Classes
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
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
  • S. Shelah
  • Mathematics
    Studies in logic and the foundations of mathematics
  • 1990
Upward Stability Transfer for Tame Abstract Elementary Classes
TLDR
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
TLDR
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
We continue here Part A, and the main results are proved here. This part deals withn-dimensional diagrams of models.
...
1
2
3
...