Jump inversions of algebraic structures and Σ‐definability

Abstract

AbstractIt 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 .