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

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
Keywords Q-reducibility   s-reducibility   hyperhyperimmune set
Categories (categorize this paper)
DOI 10.2178/jsl/1230396928
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 62,242
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

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

Add more citations

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.


Added to PP index

Total views
11 ( #823,064 of 2,444,830 )

Recent downloads (6 months)
1 ( #457,287 of 2,444,830 )

How can I increase my downloads?


My notes