The programming logic PL/CV3 is based on the notion of a mathematical type. We present the core of the type theory, from which the full theory for program verification and specification can be derived. Whereas the full theory was designed to be useable, the core theory was selected to be analyzable. This presentation strives to be succinct yet thorough. The last section consists of examples, but the approach here is not tutorial. Key Words and phrases: automated logic, program verification, program specification, semantics of programming languages, type theory, foundations of mathematics.