Toward Classifying Unstable Theories Sh500
نویسنده
چکیده
We prove a consistency results saying, that for a simple (first order) theory, it is easier to have a universal model in some cardinalities, than for the theory of linear order. We define additional properties of first order theories, the n-strong order property (SOPn in short). The main result is that a first order theory with the 4-strong order property behaves like linear orders concerning existence of universal models.
منابع مشابه
Toward Classifying Unstable Theories
We prove a consistency results saying, that for a simple (first order) theory, it is easier to have a universal model in some cardinalities, than for the theory of linear order. We define additional properties of first order theories, the n-strong order property (SOPn in short). The main result is that a first order theory with the 4-strong order property behaves like linear orders concerning e...
متن کاملToward Classifying Unstable
We prove a consistency results saying, that for a simple (first order) theory, it is easier to have a universal model in some cardinalities, than for the theory of linear order. We define additional properties of first order theories, the n-strong order property (SOPn in short). The main result is that a first order theory with the 4-strong order property behaves like linear orders concerning e...
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This paper continues [DjSh692]. We present a rank function for NSOP1 theories and give an example of a theory which is NSOP1 but not simple. We also investigate the connection between maximality in the ordering ⊳ among complete first order theories and the (N)SOP2 property. We complete the proof started in [DjSh692] of the fact that ⊳-maximality implies SOP2 and get weaker results in the other ...
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This paper investigates a connection between the ordering ⊳∗ among theories in model theory and the (N)SOPn hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP2 and SOP1, and gives a connection between SOP1 and the maximality in the ⊳∗-ordering. Together with the known results about the connection between the (N)SOPn hierarchy and the exi...
متن کاملModel Theory, Volume 47, Number 11
group Aut(M). Stability and Diophantine Geometry A structure M is said to be unstable if it interprets a bipartite graph (P,Q,R) with the feature that for each n there are ai ∈ P and bi ∈ Q for i = 1, . . . , n such that R(ai, bj ) if and only if i < j. A complete theory is unstable if some (any) model is unstable. If M is unstable (witnessed by (P,Q,R) ) and saturated, then there are ai and bi...
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