Journal of Symbolic Logic 71 (4):1394 - 1410 (2006)

Abstract
Topologists Nabutovsky and Weinberger discovered how to embed computably enumerable (c.e.) sets into the geometry of Riemannian metrics modulo diffeomorphisms. They used the complexity of the settling times of the c.e. sets to exhibit a much greater complexity of the depth and density of local minima for the diameter function than previously imagined. Their results depended on the existence of certain sequences of c.e. sets, constructed at their request by Csima and Soare, whose settling times had the necessary dominating properties. Although these computability results had been announced earlier, their proofs have been deferred until this paper. Computably enumerable sets have long been used to prove undecidability of mathematical problems such as the word problem for groups and Hilbert's Tenth Problem. However, this example by Nabutovsky and Weinberger is perhaps the first example of the use of c.e. sets to demonstrate specific mathematical or geometric complexity of a mathematical structure such as the depth and distribution of local minima
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1164060462
Options
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: 53,688
Through your library

References found in this work BETA

Computability Theory and Differential Geometry.Robert I. Soare - 2004 - Bulletin of Symbolic Logic 10 (4):457-486.
The Settling-Time Reducibility Ordering.Barbara F. Csima & Richard A. Shore - 2007 - Journal of Symbolic Logic 72 (3):1055 - 1071.
Computability Theory.Lars Kristiansen - 2007 - Studia Logica 86 (1):145-146.

Add more references

Citations of this work BETA

The Computable Lipschitz Degrees of Computably Enumerable Sets Are Not Dense.Adam R. Day - 2010 - Annals of Pure and Applied Logic 161 (12):1588-1602.

Add more citations

Similar books and articles

Computability Theory and Differential Geometry.Robert I. Soare - 2004 - Bulletin of Symbolic Logic 10 (4):457-486.
On Orbits, of Prompt and Low Computably Enumerable Sets.Kevin Wald - 2002 - Journal of Symbolic Logic 67 (2):649-678.
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.
On the Orbits of Hyperhypersimple Sets.Wolfgang Maass - 1984 - Journal of Symbolic Logic 49 (1):51-62.
Computability, Complexity, Logic.E. Börger - 1989 - New York: U.S.A.Elsevier Science Pub. Co..
Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers.Piergiorgio Odifreddi - 1989 - Sole Distributors for the Usa and Canada, Elsevier Science Pub. Co..
Recursively Enumerable Generic Sets.Wolfgang Maass - 1982 - Journal of Symbolic Logic 47 (4):809-823.

Analytics

Added to PP index
2010-08-24

Total views
46 ( #208,926 of 2,349,544 )

Recent downloads (6 months)
10 ( #63,463 of 2,349,544 )

How can I increase my downloads?

Downloads

My notes