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Paper IPM / M / 8702  


Abstract:  
Keisler in [] proved that if κ is a
strong limit cardinal and λ is a singular cardinal, then
the transfer relation κ→λ holds. We
analyze the λlike 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 λlike model
M with builtin Skolem functions that satisfies the following
two properties:
(1) M is generated by a subset C of ordertype λ.
(2) M can be written as the union of an elementary end extension
chain 〈N_{i}:i < δ〉 such that for each
i < δ, there is an initial segment C_{i} of C with
C_{i} ⊆ N_{i}, and N_{i}∩(C\C_{i})=∅.
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