JUCS - Journal of Universal Computer Science 23(6): 529-538, doi: 10.3217/jucs-023-06-0529
The Least ∑-jump Inversion Theorem for n-families
Marat Faizrahmanov‡, Iskander Kalimullin‡, Antonio Montalban§, Vadim Puzarenko|‡ Kazan (Volga Region) Federal University, Kazan, Russia§ University of California, Berkeley, United States of America| Novosibirsk State University, Novosibirsk, Russia
Corresponding author: Marat Faizrahmanov ( marat.faizrahmanov@gmail.com ) © Marat Faizrahmanov, Iskander Kalimullin, Antonio Montalban, Vadim Puzarenko. This article is freely available under the J.UCS Open Content License. Citation:
Faizrahmanov M, Kalimullin I, Montalban A, Puzarenko V (2017) The Least ∑-jump Inversion Theorem for n-families. JUCS - Journal of Universal Computer Science 23(6): 529-538. https://doi.org/10.3217/jucs-023-06-0529 |  |
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
jump of structure, enumeration jump, ∑-jump, ∑-reducibility, countable family, n-family