We develop a dimension theory for D-semianalytic sets over an arbitrary non-Archimedean complete field. Our main results are the equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in characteristic 0. We also prove a parameterized version of normalization for D-semianalytic sets.
"Dimension theory and parameterized normalization for D-semianalytic sets over non-Archimedean fields." J. Symbolic Logic 70 (2) 593 - 618, June 2005. https://doi.org/10.2178/jsl/1120224730