Notre Dame Journal of Formal Logic

Continu'ous Time Goes by Russell

Uwe Lück

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.

Article information

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

Dates
First available in Project Euclid: 17 November 2006

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

Subjects
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

Keywords
time Russell instants from events continuum interval orders axiom of choice

Citation

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


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