Definable Elements and Constants

Abstract

In mathematics, or at least in the mathematics inspired by logical methods, to know a structure means to know all sets that are definable in it. In this chapter we will take a look at the smallest nonempty sets—those that have only one element. This a specialized topic, and it is technical, but it will give us an opportunity to see in detail what domains of mathematical structures are made of and in what sense they are “given to us.”