Jump inversions of algebraic structures and Σ‐definability
M Faizrahmanov, A Kach, I Kalimullin… - Mathematical Logic …, 2019 - Wiley Online Library
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.
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.
Jump inversions of algebraic structures and Σ-definability
V Puzarenko, I Kalimullin, A Montalbán, A Kach… - dspace.kpfu.ru
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim It is proved that for every
countable structure A and a computable successor ordinal α there is a countable structure
A− α which is (Formula presented.)-least among all countable structures C such that A is Σ-
definable in the αth jump C (α). We also show that this result does not hold for the limit
ordinal α= ω. Moreover, we prove that there is no countable structure A with the degree
spectrum (Formula presented.) for (Formula presented.).
countable structure A and a computable successor ordinal α there is a countable structure
A− α which is (Formula presented.)-least among all countable structures C such that A is Σ-
definable in the αth jump C (α). We also show that this result does not hold for the limit
ordinal α= ω. Moreover, we prove that there is no countable structure A with the degree
spectrum (Formula presented.) for (Formula presented.).
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