Abstract
We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models, or existence of large cardinals). We prove (assuming a weak version of GCH around λ) that if ℜ is categorical in λ, λ+,LS(ℜ) ≤ λ and has intermediate number of models in λ++,then ℜ has a model in λ+++.
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