A trichotomy of countable, stable, unsuperstable theories
نویسنده
چکیده
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.
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 کاملN ov 2 00 7 A nonstructure theorem for countable , stable , unsuperstable theories
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.
متن کاملA model theoretic Baire category theorem for simple theories and its applications
We prove a model theoretic Baire category theorem for τ̃ f low-sets in a countable simple theory in which the extension property is firstorder and show some of its applications. We also prove a trichotomy for minimal types in countable nfcp theories: either every type that is internal in a minimal type is essentially-1-based by means of the forking topology or T interprets a strongly-minimal for...
متن کاملThe Universality Spectrum of Stable Unsuperstable Theories
4 7 r e v i s i o n : 1 9 9 6 0 3 1 9 m o d i f i e d : 1 9 9 6 0 3 1 9 The Universality Spectrum of Stable Unsuperstable Theories By Menachem Kojman and Saharon Shelah† Mathematics Department, The Hebrew University of Jerusalem, Jerusalem ABSTRACT It is shown that if T is stable unsuperstable, and א1 < λ = cfλ < 2 א0 , or 20 < μ < λ = cfλ < μ0 then T has no universal model in cardinality λ, an...
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 کامل