The term "p-adic ultrametric" is a technical phrase that often appears in mathematics. It refers to a particular metric space that is constructed using a prime number p. Within the context of mathematics, there are several synonyms that can be used to describe this concept. One alternative term that is commonly used is "non-Archimedean metric," which refers to metrics that do not satisfy the triangle inequality. Another synonym that is sometimes used is "p-adic valuation," which refers to the valuation function associated with the p-adic field. Other related terms include "p-adic norm" and "p-adic distance," both of which describe the properties of the metric space.