On Keisler singular-like models.

Keisler in [7] proved that for a strong limit cardinal κ and a singular cardinal λ, the transfer relation κ → λ holds. We analyze the λ -like models produced in the proof of Keisler's transfer theorem when κ is further assumed to be regular. Our main result shows that with this extra assumption, Keisler's proof can be modified to produce a λ -like model M with built-in Skolem functions that satisfies the following two properties: (1) M is generated by a subset C of order-type λ. (2) M can be written as union of an elementary end extension chain 〈Ni: i < δ 〉 such that for each i < δ, there is an initial segment Ci of C with Ci ⊆ Ni, and Ni ∩ (C \Ci) = ∅. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]