David Gonzalez

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20242026

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4 papers · 1 filter

math.LO2026

Recovering a structure from its tree of tuples

David Gonzalez, Matthew Harrison-Trainor, Julia Knight

We show that for each countable ordinal $α$ , there is a $Δ_{α}^{0}$ operator that, for all $A$ of Scott rank at most $α$ , takes copies of $T_{A}$ to copies of $A$ , where $T_{A}$ is…

math.LO2025

Optimal Syntactic Definitions of Back-and-Forth Types

Ruiyuan Chen, David Gonzalez, Matthew Harrison-Trainor

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

math.LO2024

Scott Spectral Gaps are Bounded for Linear Orderings

David Gonzalez, Matthew Harrison-Trainor

We demonstrate that any $Π_{α}$ sentence of the infinitary logic $L_{ω_{1} ω}$ extending the theory of linear orderings has a model with a $Π_{α + 4}$ Scott sentence and hence of Scott r…

math.LO2024

Scott analysis, linear orders and almost periodic functions

David Gonzalez, Matthew Harrison-Trainor, Meng-Che "Turbo" Ho

For any limit ordinal $λ$ , we construct a linear order $L_{λ}$ whose Scott complexity is $Σ_{λ + 1}$ . This completes the classification of the possible Scott sentence complexities of l…