Jump inversions of algebraic structures and Σ‐definability |
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Authors: | Marat Faizrahmanov,Asher Kach,Iskander Kalimullin,Antonio Montalb n,Vadim Puzarenko |
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Affiliation: | Marat Faizrahmanov,Asher Kach,Iskander Kalimullin,Antonio Montalbán,Vadim Puzarenko |
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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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