Submission date: 7 July 2015.

Abstract:

In this paper we prove:

Theorem 1. Let K be an abstract elementary class which satisfies the joint embedding and amalgamation properties. Suppose λ > μ ≥ LS(K) and θ is a limit ordinal < λ^+. If K is μ-superstable and μ^+-superstable and satisfies μ^+-symmetry, then for any increasing and continuous sequence ⟨ M_i | i<θ ⟩ of μ^+-saturated models of cardinality λ, the model ∪_{i<θ}M_i is μ^+-saturated.

Mathematics Subject Classification:

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Full text arXiv 1507.01989: pdf, ps.