The Least ∑-jump Inversion Theorem for n-families

The Least ∑-jump Inversion Theorem for n-families Full article

Journal

Journal of Universal Computer Science
ISSN: 0948-695X , E-ISSN: 0948-6968

Output data

Year: 2017, Volume: 23, Number: 6, Pages: 529-538 Pages count : 10 DOI: 10.3217/jucs-023-06-0529

Tags

jump of structure, enumeration jump, Σ-jump, Σ-reducibility, countable family, n-family

Authors

Faizrahmanov Marat ³ , Kalimullin Iskander ³ , Montalban Antonio ⁴ , Puzarenko Vadim ^1,2

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University
3	Kazan (Volga Region) Federal University
4	University of California Berkley

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).

Faizrahmanov M. , Kalimullin I. , Montalban A. , Puzarenko V.
The Least ∑-jump Inversion Theorem for n-families
Journal of Universal Computer Science. 2017. V.23. N6. P.529-538. DOI: 10.3217/jucs-023-06-0529

Submitted:	Apr 3, 2017
Accepted:	Jun 26, 2017
Published online:	Jun 28, 2017

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