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  1. The Structural Complexity of Models of Arithmetic.Antonio Montalbán & Dino Rossegger - forthcoming - Journal of Symbolic Logic:1-17.
    We calculate the possible Scott ranks of countable models of Peano arithmetic. We show that no non-standard model can have Scott rank less than $\omega $ and that non-standard models of true arithmetic must have Scott rank greater than $\omega $. Other than that there are no restrictions. By giving a reduction via $\Delta ^{\mathrm {in}}_{1}$ bi-interpretability from the class of linear orderings to the canonical structural $\omega $ -jump of models of an arbitrary completion T of $\mathrm {PA}$ we (...)
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  • The classification of countable models of set theory.John Clemens, Samuel Coskey & Samuel Dworetzky - 2020 - Mathematical Logic Quarterly 66 (2):182-189.
    We study the complexity of the classification problem for countable models of set theory (). We prove that the classification of arbitrary countable models of is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well‐founded models of.
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