A note on trivial nonmultidimensional superstable theories

1995 ◽  
Vol 34 (1) ◽  
pp. 21-31
Author(s):  
Ambar Chowdhury
Keyword(s):  
Superstable Theories

Notes on the stability of separably closed fields

1979 ◽  
Vol 44 (3) ◽  
pp. 412-416 ◽  
Author(s):  
Carol Wood
Keyword(s):  
Differential Algebra ◽  
Complete Theory ◽  
Model Completeness ◽  
Closed Fields ◽  
Superstable Theories ◽  
Basic Facts ◽  
The Stability ◽  
Differential Fields

AbstractThe stability of each of the theories of separably closed fields is proved, in the manner of Shelah's proof of the corresponding result for differentially closed fields. These are at present the only known stable but not superstable theories of fields. We indicate in §3 how each of the theories of separably closed fields can be associated with a model complete theory in the language of differential algebra. We assume familiarity with some basic facts about model completeness [4], stability [7], separably closed fields [2] or [3], and (for §3 only) differential fields [8].

Countable models of trivial theories which admit finite coding

1996 ◽  
Vol 61 (4) ◽  
pp. 1279-1286 ◽  
Author(s):  
James Loveys ◽  
Predrag Tanović
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Superstable Theories ◽  
Countable Models

AbstractWe prove:Theorem. A complete first order theory in a countable language which is strictly stable, trivial and which admits finite coding hasnonisomorphic countable models.Combined with the corresponding result or superstable theories from [4] our result confirms the Vaught conjecture for trivial theories which admit finite coding.

Superstable theories with few countable models

1992 ◽  
Vol 31 (6) ◽  
pp. 457-465 ◽  
Author(s):  
Lee Fong Low ◽  
Anand Pillay
Keyword(s):  
Superstable Theories ◽  
Countable Models

Some remarks on nonmultidimensional superstable theories

1994 ◽  
Vol 59 (1) ◽  
pp. 151-165 ◽  
Author(s):  
Anand Pillay
Keyword(s):  
General Theory ◽  
Finite Rank ◽  
Atomic Model ◽  
Elementary Substructure ◽  
Finite Dimensional ◽  
Definable Groups ◽  
Superstable Theories ◽  
Finite Dimensional Case ◽  
Language Context ◽  
Minimal Formula

In this paper we study nonmultidimensional superstable theories T, possibly in an uncountable language, and develop some techniques permitting the generalisation of certain results from the finite rank (and/or countable language) context to the general case.We prove, among other things, the following: there is a set A0 of parameters, which has cardinality at most ∣T∣, and in the finite-dimensional case is finite, such that over any B ⊇ A0 there is a locally atomic model. One of the consequences of this is that if C is the monster model of T, φ(x) is a formula over A0, φC ⊇ X and (X, φC) satisfies the Tarski-Vaught condition after adding names for A0, then there is an elementary substructure M of C containing A0 such that φM = X. Applications to the spectrum problem will appear in [Ch-P].In fact, all the components of the machinery we develop are already present in the general theory. One such component involves a stratification of the regular types of T using a generalized notion of weakly minimal formula. This appears in [Sh, Chapter V and the proof of IX.2.4] and also in [P2]. A second component involves definable groups which arise as ‘binding” groups. The existence of such groups, under certain hypotheses on the behavior of nonorthogonality, is due to Hrushovski [Hr1], and our use of them to help obtain “j-constructible” models is similar to their use in [Bu-Sh].

Countable models of superstable theories

1990 ◽  
Vol 29 (3) ◽  
pp. 181-192 ◽  
Author(s):  
E. R. Baisalov
Keyword(s):  
Superstable Theories ◽  
Countable Models
Sign in / Sign up

Export Citation Format

Share Document