  It is shown that the skew field of Malcev-Neumann series of an ordered group
frequently contains a free field of countable rank, i.e. the universal field of
fractions of a free associative algebra of countable rank. This is an
application of a criterion on embeddability of free fields on skew fields which
are complete with respect to a valuation function, following K. Chiba. Other
applications to skew Laurent series rings are discussed. Finally, embeddability
questions on free fields of uncountable rank in Malcev-Neumann series rings are
also considered.
