Existentially equivalent cyclic ultrametric spaces and cyclically valued groups

The notions of ultrametric distances and cyclic valuations appear when the set of values of the distance map is a cyclically ordered set. These structures can be described as subspaces of cartesian products. In this paper we characterize existentially equivalence between cyclically ultrametric spaces, as well as existentially equivalence between generalized ultrametric spaces. We also describe classes of existentially equivalent cyclically valued groups.