Minimal and Order-Minimal Structures

Abstract

Before we get into details regarding number structures, we will examine definability in cases that are easier to analyze. We define two important classes of structures: minimal, in Definition 9.1, and order-minimal, in Definition 9.4. The important concepts of type and symmetry were already introduced in Chap. 2; here we define them in general model-theoretic terms and use them to analyze the orderings of the sets of natural numbers, integers, and rationals.