The Least ∑-jump Inversion Theorem for n-families

Marat Faizrahmanov (Kazan (Volga Region) Federal University, Russia)

Iskander Kalimullin (Kazan (Volga Region) Federal University, Russia)

Antonio Montalban (University of California, USA)

Vadim Puzarenko (Novosibirsk State University, Russia)

Abstract: Studying the ∑-reducibility of families introduced by [Kalimullin and Puzarenko 2009] we show that for every set there is a family of sets which is the ∑-least countable family whose ∑-jump is ∑-equivalent to . This fact will be generalized for the class of n-families (families of families of ... of sets).

Keywords: n-family, countable family, enumeration jump, jump of structure, ∑-jump, ∑-reducibility

Categories: F.1.1, F.1.2, F.4.1