  Through a cascade of generalizations, we develop a theory of motivic
integration which works uniformly in all non-archimedean local fields of
characteristic zero, overcoming some of the difficulties related to
ramification and small residue field characteristics. We define a class of
functions, called functions of motivic exponential class, which we show to be
stable under integration and under Fourier transformation, extending results
and definitions from previous papers. We prove uniform results related to
rationality and to various kinds of loci. A key ingredient is a refined form of
Denef-Pas quantifier elimination which allows us to understand definable sets
in the value group and in the valued field.
