Closed asymptotic couples

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.