The Settling-Time Reducibility Ordering

Journal of Symbolic Logic 72 (3):1055 - 1071 (2007)
  Copy   BIBTEX


To each computable enumerable (c.e.) set A with a particular enumeration {As}s∈ω, there is associated a settling function mA(x), where mA(x) is the last stage when a number less than or equal to x was enumerated into A. One c.e. set A is settling time dominated by another set B (B >st A) if for every computable function f, for all but finitely many x, mB(x) > f(m₄(x)). This settling-time ordering, which is a natural extension to an ordering of the idea of domination, was first introduced by Nabutovsky and Weinberger in [3] and Soare [6]. They desired a sequence of sets descending in this relationship to give results in differential geometry. In this paper we examine properties of the <st ordering. We show that it is not invariant under computable isomorphism, that any countable partial ordering embeds into it, that there are maximal and minimal sets, and that two c.e. sets need not have an inf or sup in the ordering. We also examine a related ordering, the strong settling-time ordering where we require for all computable f and g, for almost all x, mB(x) > f(mA(g(x)))



    Upload a copy of this work     Papers currently archived: 93,296

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


Added to PP

11 (#1,167,245)

6 months
24 (#121,857)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Computability Results Used in Differential Geometry.Barbara F. Csima & Robert I. Soare - 2006 - Journal of Symbolic Logic 71 (4):1394 - 1410.

Add more citations

References found in this work

Computability theory and differential geometry.Robert I. Soare - 2004 - Bulletin of Symbolic Logic 10 (4):457-486.

Add more references