N ov 2 00 7 A nonstructure theorem for countable , stable , unsuperstable theories
نویسنده
چکیده
A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a ‘regular ideal’ of formulas and study types that are minimal with respect to such an ideal.
منابع مشابه
A nonstructure theorem for countable, stable, unsuperstable theories
A trichotomy theorem for countable, stable, unsuperstable theories is proved. We develop the notion of a ‘regular ideal’ of formulas and study types that are minimal with respect to such an ideal.
متن کاملConstructing Strongly Equivalent Nonisomorphic Models for Unsuperstable Theories, Part C
In this paper we prove a strong nonstructure theorem for κ(T )-saturated models of a stable theory T with dop. This paper continues the work started in [HT].
متن کاملOn the Number of Elementary Submodels of an Unsuperstable Homogeneous Structure
We show that if M is a stable unsuperstable homogeneous structure, then for most κ < |M| , the number of elementary submodels of M of power κ is 2 . Through out this paper we assume that M is a stable unsuperstable homogeneous model such that |M| is strongly inaccessible (= regular and strong limit). We can drop this last assumption if instead of all elementary submodels of M we study only suit...
متن کاملA trichotomy of countable, stable, unsuperstable theories
Every countable, strictly stable theory either has the Dimensional Order Property (DOP), is deep, or admits an ‘abelian group witness to unsuperstability’. To obtain this and other results, we develop the notion of a ‘regular ideal’ of formulas and study types that are minimal with respect to such an ideal.
متن کامل0 N ov 2 00 5 UPWARD STABILITY TRANSFER FOR TAME ABSTRACT ELEMENTARY CLASSES
Grossberg and VanDieren have started a program to develop a stability theory for tame classes (see [GrVa1]). We name some variants of tameness (Definitions 1.4 and 1.7) and prove the following. Theorem 0.1. Let K be an AEC with Löwenheim-Skolem number ≤ κ. Assume that K satisfies the amalgamation property and is κ-weakly tame and Galois-stable in κ. Then, K is Galois-stable in κ for all n < ω. ...
متن کامل