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math.LO2024
Scott Spectral Gaps are Bounded for Linear Orderings
David Gonzalez, Matthew Harrison-Trainor
We demonstrate that any sentence of the infinitary logic extending the theory of linear orderings has a model with a 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 , we construct a linear order whose Scott complexity is . This completes the classification of the possible Scott sentence complexities of l…