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2014 Lowness for Difference Tests
David Diamondstone, Johanna N. Y. Franklin
Notre Dame J. Formal Logic 55(1): 63-73 (2014). DOI: 10.1215/00294527-2377878

Abstract

We show that being low for difference tests is the same as being computable and therefore lowness for difference tests is not the same as lowness for difference randomness. This is the first known example of a randomness notion where lowness for the randomness notion and lowness for the test notion do not coincide. Additionally, we show that for every incomputable set A, there is a difference test TA relative to A which cannot even be covered by finitely many unrelativized difference tests.

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David Diamondstone. Johanna N. Y. Franklin. "Lowness for Difference Tests." Notre Dame J. Formal Logic 55 (1) 63 - 73, 2014. https://doi.org/10.1215/00294527-2377878

Information

Published: 2014
First available in Project Euclid: 20 January 2014

zbMATH: 1330.03078
MathSciNet: MR3161412
Digital Object Identifier: 10.1215/00294527-2377878

Subjects:
Primary: 03D32

Rights: Copyright © 2014 University of Notre Dame

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