A characterization of the Δ⁰₂ hyperhyperimmune sets

Journal of Symbolic Logic 73 (4):1407-1415 (2008)
  Copy   BIBTEX

Abstract

Let A be an infinite Δ₂⁰ set and let K be creative: we show that K≤Q A if and only if K≤Q₁ A. (Here ≤Q denotes Q-reducibility, and ≤Q₁ is the subreducibility of ≤Q obtained by requesting that Q-reducibility be provided by a computable function f such that Wf(x)∩ Wf(y)=∅, if x \not= y.) Using this result we prove that A is hyperhyperimmune if and only if no Δ⁰₂ subset B of A is s-complete, i.e., there is no Δ⁰₂ subset B of A such that \overline{K}≤s B, where ≤s denotes s-reducibility, and \overline{K} denotes the complement of K

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,215

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The degrees of hyperhyperimmune sets.Carl G. Jockusch - 1969 - Journal of Symbolic Logic 34 (3):489-493.
The ordertype of β-r.E. Sets.Klaus Sutner - 1990 - Journal of Symbolic Logic 55 (2):573-576.
On modal μ-calculus and non-well-founded set theory.Luca Alberucci & Vincenzo Salipante - 2004 - Journal of Philosophical Logic 33 (4):343-360.
Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry.John P. Burgess - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.
Computational randomness and lowness.Sebastiaan A. Terwijn & Domenico Zambella - 2001 - Journal of Symbolic Logic 66 (3):1199-1205.
Mathias absoluteness and the Ramsey property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
Characterization of recursively enumerable sets.Jesse B. Wright - 1972 - Journal of Symbolic Logic 37 (3):507-511.
Characterizing the Join-Irreducible Medvedev Degrees.Paul Shafer - 2011 - Notre Dame Journal of Formal Logic 52 (1):21-38.

Analytics

Added to PP
2010-09-12

Downloads
11 (#845,670)

6 months
1 (#449,220)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Agreement reducibility.Rachel Epstein & Karen Lange - 2020 - Mathematical Logic Quarterly 66 (4):448-465.

Add more citations

References found in this work

No references found.

Add more references