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- Title
Jump inversions of algebraic structures and Σ‐definability.
- Authors
Faizrahmanov, Marat; Kach, Asher; Kalimullin, Iskander; Montalbán, Antonio; Puzarenko, Vadim
- Abstract
It is proved that for every countable structure A and a computable successor ordinal α there is a countable structure A−α which is ≤Σ‐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 {d:a≤d(ω)} for a>0(ω).
- Subjects
INVERSIONS (Geometry); MATHEMATICS theorems; DEFINABILITY theory (Mathematical logic); MATHEMATICAL induction; ISOMORPHISM (Mathematics)
- Publication
Mathematical Logic Quarterly, 2019, Vol 65, Issue 1, p37
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.201800015