I'm looking for a reference that surveys (as generally as possible) the various notions of 'completion' for an ordered space and their relation to eachother.
In particular, I'd like a reference that covers notions like pseudo-convergent completion in relation to notions like Dedekind and Archimedean completion for ordered fields. I'm aware of the excellent paper by Philip Ehrlich discussing the latter two notions and their relationship in depth, but it does not appear to touch on pseudo-convergent completion or its relation to the other two.
Even more particularly, I'd like a reference on how the value class of a non-Archimedean field is effected by the various notions of completion. Pseudo-convergent completion leaves the value class unchanged while possibly adding new elements with a given valuation to the underlying field; I would like to know if other types of completion can canonically extend the value class of a non-Archimedean ordered field.