On Types over p-­adically Closed Fields

Studies in Logic, Vol. 16, No. 6 (2023): 58–73                     PII: 1674­3202(2023)­06­0058­16

Ningyuan Yao, Zhentao Zhang

Abstract. The aim of this paper is to study types over a p­-adically closed field. We classify the 1­types over an arbitrary p-­adically closed field, which extends the previous work of Penazzi, Pillay and Yao (2019) on classifying 1­types over the standard model of the field of p-­adic numbers. We also study the orthogonality of pseudo­limit types and distance types and yield an analogue of the dichotomy of “cuts” and “noncuts” in the o-­minimal context.