Order-Invariant Types and their Applications

Abstract

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, hut not actually dependent on that order relation. This is somewhat surprising since order-invariant properties are more of a. combinatorial rather than a logical object. We provide two applications of this notion. One is a proof, from the basic principles, of a, theorem by Courcelle stating that over trees, order-invariant NISO properties are expressible in IMO