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2006 Continu'ous Time Goes by Russell
Uwe Lück
Notre Dame J. Formal Logic 47(3): 397-434 (2006). DOI: 10.1305/ndjfl/1163775446

Abstract

Russell and Walker proposed different ways of constructing instants from events. For an explanation of "time as a continuum," Thomason favored Walker's construction. The present article shows that Russell's construction fares as well. To this end, a mathematical characterization problem is solved which corresponds to the characterization problem that Thomason solved with regard to Walker's construction. It is shown how to characterize those event structures (formally, interval orders) which, through Russell's construction of instants, become linear orders isomorphic to a given (or, deriving, to some—nontrivial ordered) real interval. As tools, separate characterizations for each of resulting (i) Dedekind completeness, (ii) separability, (iii) plurality of elements, (iv) existence of certain endpoints are provided. Denseness is characterized to replace Russell's erroneous attempt. Somewhat minimal nonconstructive principles needed are exhibited, and some alternative approaches are surveyed.

Citation

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Uwe Lück. "Continu'ous Time Goes by Russell." Notre Dame J. Formal Logic 47 (3) 397 - 434, 2006. https://doi.org/10.1305/ndjfl/1163775446

Information

Published: 2006
First available in Project Euclid: 17 November 2006

zbMATH: 1113.03012
MathSciNet: MR2264708
Digital Object Identifier: 10.1305/ndjfl/1163775446

Subjects:
Primary: 06A99
Secondary: 01A60, 03C52, 03E17, 03E25, 06A05

Rights: Copyright © 2006 University of Notre Dame

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Vol.47 • No. 3 • 2006
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