Optimal Syntactic Definitions of Back-and-Forth Types

Ruiyuan Chen, David Gonzalez, Matthew Harrison-Trainor

The back-and-forth relations $M{\le }_{\alpha }N$ are central to computable structure theory and countable model theory. It is well-known that the relation $\{(M,N):M{\le }_{\alpha }N\}$ is (lightf…