Jump inversions of algebraic structures and Σ‐definability

Mathematical Logic Quarterly 65 (1):37-45 (2019)
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Abstract

It is proved that for every countable structure and a computable successor ordinal α there is a countable structure which is ‐least among all countable structures such that is Σ‐definable in the αth jump. We also show that this result does not hold for the limit ordinal. Moreover, we prove that there is no countable structure with the degree spectrum for.

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References found in this work

Generic copies of countable structures.Chris Ash, Julia Knight, Mark Manasse & Theodore Slaman - 1989 - Annals of Pure and Applied Logic 42 (3):195-205.
The jump operation for structure degrees.V. Baleva - 2005 - Archive for Mathematical Logic 45 (3):249-265.

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