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| Paper IPM / M / 8702 |
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| Abstract: | |
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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 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 the 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)=∅.
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