The Turing Degrees and Keisler’s Order

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Journal of Symbolic Logic 89 (1):331-341 (2024)
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Abstract

There is a Turing functional $\Phi $ taking $A^\prime $ to a theory $T_A$ whose complexity is exactly that of the jump of A, and which has the property that $A \leq _T B$ if and only if $T_A \trianglelefteq T_B$ in Keisler’s order. In fact, by more elaborate means and related theories, we may keep the complexity at the level of A without using the jump.

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10.1017/jsl.2022.63

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References found in this work

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Ultraproducts which are not saturated.H. Jerome Keisler - 1967 - Journal of Symbolic Logic 32 (1):23-46.
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A primer of simple theories.Rami Grossberg, José Iovino & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (6):541-580.
Hypergraph sequences as a tool for saturation of ultrapowers.M. E. Malliaris - 2012 - Journal of Symbolic Logic 77 (1):195-223.

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