  In this note, we study substructures of generalised power series fields
induced by families of well-ordered subsets of the group of exponents. We
characterise the set-theoretic and algebraic properties of the induced
substructures in terms of conditions on the families. We extend the work of
Rayner by giving both \emph{necessary} and sufficient conditions to obtain
truncation closed subgroups, subrings and subfields.
