In classical logic, distal structures are a kind of first-order structures, including ordered structures like the real field as well as ordered-ish structures like the p-adic valued field.

 

Distal structures have many different definitions. They can be characterized by their innately ordered indiscernible sequences, or by several aspects of the combinatorics of their definable sets. We will explore how these properties of distal structures extend to the context of metric structures, and find out how discrete combinatorics translates to continuous logic.