  In this paper we introduce a model theoretic construction for the theories of
uniform layered domains and semifields introduced in the paper of Izhakian,
Knebusch and Rowen. We prove that, for a given layering semiring L, the theory
of uniform L-layered divisibly closed semifields is complete. In the process of
doing so, we prove that this theory has quantifier elimination and consequently
is model complete. Model completeness of uniform L-layered divisibly closed has
some important consequences regarding the uniform L-layered semifields theory.
One example involves equating polynomials. Namely, model completeness insures
us that if two polynomials are equal over a divisibly closed uniform L-layered
semifield, then they are equal over any divisibly closed uniform L-layered
extension of that semifield, and thus over any uniform L-layered domain
extending the semifield (as it is contained in its divisible closure of its
semifield of fractions). At the end of this paper we apply our results to the
theory of max-plus algebras as a special case of uniform L -layered domains.
