Independence, dimension and continuity in non-forking frames. (English) Zbl 1315.03048

Summary: The notion \(J\) is independent in \((M,M_0,N)\) was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal \(\lambda\) and has a non-forking relation, satisfying the good \(\lambda\)-frame axioms and some additional hypotheses. Shelah uses independence to define dimension.
Here, we show the connection between the continuity property and dimension: if a non-forking satisfies natural conditions and the continuity property, then the dimension is well-behaved.
As a corollary, we weaken the stability hypothesis and two additional hypotheses, that appear in Shelah’s theorem.


03C45 Classification theory, stability, and related concepts in model theory
03C48 Abstract elementary classes and related topics
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