Continu'ous Time Goes by Russell
Uwe Lück
Source: Notre Dame J. Formal Logic Volume 47, Number 3
(2006), 397-434.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1163775446
Digital Object Identifier: doi:10.1305/ndjfl/1163775446
Mathematical Reviews number (MathSciNet): MR2264708
Zentralblatt MATH identifier: 1113.03012
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