The least Σ-jump inversion theorem for N-families

Abstract

© J.UCS. Studying the Σ-reducibility of families introduced by [Kalimullin and Puzarenko 2009] we show that for every set X ≥ T ∅׳_there is a family of sets F which is the Σ-least countable family whose Σ-jump is Σ-equivalent to X ⊕ X. This fact will be generalized for the class of n-families (families of families of… of sets).