David Gonzalez

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math.LO2025

Optimal Syntactic Definitions of Back-and-Forth Types

Ruiyuan Chen, David Gonzalez, Matthew Harrison-Trainor

The back-and-forth relations $M \leq_{I^} \pm N$ are central to computable structure theory and countable model theory. It is well-known that the relation ${(M, N) : M \leq_{I^} \pm N}$ is (ligh…

math.LO2025

Scott Spectral Gaps are Bounded for Linear Orderings

David Gonzalez, Matthew Harrison-Trainor

We demonstrate that any $I^_{I^} \pm$ sentence of the infinitary logic $L_{I ¨ _{1} I ¨ }$ extending the theory of linear orderings has a model with a $I^_{I^\pm+ 4}$ Scott sentence and hence of S…