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Paper   IPM / M / 7340
School of Mathematics
  Title:   Joint embedding and amalgamation for certain classes of ordered fields
1.  S. M. Bagheri
2.  Moj. Moniri
  Status:   Published
  Journal: J. Appl. Algebra Discrete Struct.
  Vol.:  3
  Year:  2005
  Pages:   159-167
  Supported by:  IPM
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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