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THE TURING DEGREES AND KEISLER’S ORDER
Part of
- Model theory
- Computability and recursion theory
MARYANTHE MALLIARIS, SAHARON SHELAH
Journal:

The Journal of Symbolic Logic / Volume 89 / Issue 1 / March 2024

Published online by Cambridge University Press:

07 September 2022, pp. 331-341

Print publication:

March 2024
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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.