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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
$\lambda$, the family of real closed, Archimedean complete ordered
fields of cofinality $\lambda$ 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 $\lambda$ or $\leq \lambda$ has JEP and
AP. Observing AP for Archimedean ordered fields, the question is
raised whether the class of $\lambda$-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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