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| Paper IPM / M / 7340 |
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| Abstract: | |||||
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The class of real closed field having JEP and AP implies the same
for the class OF of ordered fields. For any regular cardinal
λ, the family of real closed, Archimedean complete ordered
fields of cofinality λ is cofinal in OF. Therefore any
subclass of OF containing that family has JEP and AP. E.g.
either of the classes of Scott complete, Archimedean complete,
non-rigid, p-real closed (p a positive integer) ordered fields
or, those of cofinality λ or ≤ λ has JEP and
AP. Observing AP for Archimedean ordered fields, the question is
raised whether the class of λ-Archimedean ones has JEP or
AP. Variants of JEP and AP by restricting the embeddings to be
dense or cofinal are also mentioned.
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