Notre Dame Journal of Formal Logic

Continu'ous Time Goes by Russell

Uwe Lück


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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Notre Dame J. Formal Logic, Volume 47, Number 3 (2006), 397-434.

First available in Project Euclid: 17 November 2006

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Primary: 06A99: None of the above, but in this section
Secondary: 01A60: 20th century 03C52: Properties of classes of models 03E17: Cardinal characteristics of the continuum 03E25: Axiom of choice and related propositions 06A05: Total order

time Russell instants from events continuum interval orders axiom of choice


Lück, Uwe. Continu'ous Time Goes by Russell. Notre Dame J. Formal Logic 47 (2006), no. 3, 397--434. doi:10.1305/ndjfl/1163775446.

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