The derivation of a Hardy field induces on its value group a certain functi
on psi. If a Hardy field extends the real field and is closed under powers,
then its value group is also a vector space over R. Such "ordered vector s
paces with psi-function" are called H-couples. We define closed H-couples a
nd show that every H-couple can be embedded into a closed one. The key fact
is that closed H-couples have an elimination theory: solvability of an arb
itrary system of equations and inequalities (built up from vector space ope
rations, the function psi, parameters, and the unknowns to be solved for) i
s equivalent to an effective condition on the parameters of the system. The
H-couple of a maximal Hardy field is closed, and this is also the case for
the H-couple of the field of logarithmic-exponential series over R. We ana
lyze in detail finitely generated extensions of a given H-couple. (C) 2000
Academic Press.