Few non minimal types and non-structure

by Shelah. [Sh:603]
Proc 11 International Congress of Logic, Methodology and Philosophy of Science, Krakow August'99; In the Scope of Logic, Methodology and Philosophy of Science, 2002
We pay two debts from [Sh:576]. The main demands little knowledge from [Sh:576], just quoting a model theoretic consequence of the weak diamond. We assume that K has amalgamation in lambda, and that the minimal types are not dense to get many non-isomorphic models in lambda^+ . For this also pcf considerations are relevant. The minor debt was the use in one point of [Sh:576] of lambda ne aleph_0, it is minor as for this case by [Sh:88] we ``usually'' know more.


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