Immunity and Hyperimmunity for Sets of Minimal Indices

Notre Dame Journal of Formal Logic 49 (2):107-125 (2008)
  Copy   BIBTEX

Abstract

We extend Meyer's 1972 investigation of sets of minimal indices. Blum showed that minimal index sets are immune, and we show that they are also immune against high levels of the arithmetic hierarchy. We give optimal immunity results for sets of minimal indices with respect to the arithmetic hierarchy, and we illustrate with an intuitive example that immunity is not simply a refinement of arithmetic complexity. Of particular note here are the fact that there are three minimal index sets located in Π3 − Σ3 with distinct levels of immunity and that certain immunity properties depend on the choice of underlying acceptable numbering. We show that minimal index sets are never hyperimmune; however, they can be immune against the arithmetic sets. Lastly, we investigate Turing degrees for sets of random strings defined with respect to Bagchi's size-function s

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 107,589

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

Bounded Immunity and Btt‐Reductions.Stephen Fenner & Marcus Schaefer - 1999 - Mathematical Logic Quarterly 45 (1):3-21.
On the Turing degrees of minimal index sets.Jason Teutsch - 2007 - Annals of Pure and Applied Logic 148 (1):63-80.
Constructivity conditions on immune sets.John Case - forthcoming - Archive for Mathematical Logic:1-23.
Totally non‐immune sets.Athanassios Tzouvaras - 2015 - Mathematical Logic Quarterly 61 (1-2):103-116.
Tame Topology over dp-Minimal Structures.Pierre Simon & Erik Walsberg - 2019 - Notre Dame Journal of Formal Logic 60 (1):61-76.

Analytics

Added to PP
2010-08-24

Downloads
75 (#320,990)

6 months
20 (#194,737)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

An incomplete set of shortest descriptions.Frank Stephan & Jason Teutsch - 2012 - Journal of Symbolic Logic 77 (1):291-307.

Add more citations