  This paper is about the logarithmic limit sets of real semi-algebraic sets,
and, more generally, about the logarithmic limit sets of sets definable in an
o-minimal, polynomially bounded structure. We prove that most of the properties
of the logarithmic limit sets of complex algebraic sets hold in the real case.
This include the polyhedral structure and the relation with the theory of
non-archimedean fields, tropical geometry and Maslov dequantization.
