Mathematical Logic Quarterly 53 (4):483-492 (2007)

Abstract
We examine the concept of almost everywhere domination from the viewpoint of mass problems. Let AED and MLR be the sets of reals which are almost everywhere dominating and Martin-Löf random, respectively. Let b1, b2, and b3 be the degrees of unsolvability of the mass problems associated with AED, MLR × AED, and MLR ∩ AED, respectively. Let [MATHEMATICAL SCRIPT CAPITAL P]w be the lattice of degrees of unsolvability of mass problems associated with nonempty Π01 subsets of 2ω. Let 1 and 0 be the top and bottom elements of [MATHEMATICAL SCRIPT CAPITAL P]w. We show that inf, inf, and inf belong to [MATHEMATICAL SCRIPT CAPITAL P]w and 0 < inf < inf < inf < 1. Under the natural embedding of the recursively enumerable Turing degrees into [MATHEMATICAL SCRIPT CAPITAL P]w, we show that inf and inf but not inf are comparable with some recursively enumerable Turing degrees other than 0 and 0′. In order to make this paper more self-contained, we exposit the proofs of some recent theorems due to Hirschfeldt, Miller, Nies, and Stephan
Keywords domination  mass problems  Martin‐Löf randomness  almost everywhere domination  pseudojum  Randomness
Categories (categorize this paper)
DOI 10.1002/malq.200710013
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 50,287
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

Mass Problems and Randomness.Stephen G. Simpson - 2005 - Bulletin of Symbolic Logic 11 (1):1-27.
Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.

Add more references

Citations of this work BETA

Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Mass Problems and Hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
Demuth Randomness and Computational Complexity.Antonín Kučera & André Nies - 2011 - Annals of Pure and Applied Logic 162 (7):504-513.
Benign Cost Functions and Lowness Properties.Noam Greenberg & André Nies - 2011 - Journal of Symbolic Logic 76 (1):289 - 312.
Mass Problems and Measure-Theoretic Regularity.Stephen G. Simpson - 2009 - Bulletin of Symbolic Logic 15 (4):385-409.

View all 7 citations / Add more citations

Similar books and articles

Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Mass Problems and Randomness.Stephen G. Simpson - 2005 - Bulletin of Symbolic Logic 11 (1):1-27.
Non-Domination and Egalitarian Welfare Politics.Lena Halldenius - 1998 - Ethical Theory and Moral Practice 1 (3):335-353.
A Non-Normative Theory of Power and Domination.Pamela Pansardi - 2013 - Critical Review of International Social and Political Philosophy 16 (5):1-20.
Leibniz and Monadic Domination.Shane Duarte - 2013 - Oxford Studies in Early Modern Philosophy 6:209-48.
Non-Domination and Pure Negative Liberty.M. D. Harbour - 2012 - Politics, Philosophy and Economics 11 (2):186-205.
Lowness and $\Pi _{2}^{0}$ Nullsets.Rod Downey, Andre Nies, Rebecca Weber & Liang Yu - 2006 - Journal of Symbolic Logic 71 (3):1044 - 1052.
Republicanism and Geopolitical Domination.Mark Rigstad - 2011 - Journal of Political Power 4 (2):279-300.
But Who Created the Controllers? Control as Social Production of Meanings of Consumption.Shay Hershkovitz - 2013 - Telos: Critical Theory of the Contemporary 2013 (163):171-186.
Impunity and Domination: A Puzzle for Republicanism.R. B. Talisse - 2014 - European Journal of Political Theory 13 (2):121-131.

Analytics

Added to PP index
2013-12-01

Total views
33 ( #290,137 of 2,325,990 )

Recent downloads (6 months)
1 ( #658,522 of 2,325,990 )

How can I increase my downloads?

Downloads

My notes