We give necessary and sufficient conditions for a polynomially bounded
o-minimal expansion of a real closed field (in a language of arbitrary
cardinality) to be ℵα​-saturated. The conditions are in terms of
the value group, residue field, and pseudo- Cauchy sequences of the natural
valuation on the real closed field. This is achieved by an analysis of types,
leading to the trichotomy. Our characterization provides a construction method
for saturated models, using fields of generalized power series.Comment: Key words and phrases. natural valuation, value group, residue field,
pseudo- Cauchy sequences, polynomially bounded o-minimal expansion of a real
closed field, definable closure, dimension, saturation. To appear in Algebra
and Logic volume 54 Issue 5 November 201