 To accomplish these goals, we presuppose only a familiarity with the first-order predicate calculus. We show how to extend this language and logic to the second-order predicate calculus, and show how to represent the ideas and claims involved in Frege’s Theorem in this calculus. These ideas and claims all appear in Frege 1893/1903, which we refer to as Gg I/II. But we sometimes also cite his book of 1879 and his book of 1884 (Die Grundlagen der Arithmetik), referring to these works as Begr and Gl, respectively.