Continu'ous Time Goes by Russell

Russell and Walker proposed different ways of constructing instants from events. As an explanation of “time as a continuum”, Thomason favoured Walker’s construction. The present paper 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–non-trivial 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 non-constructive principles needed are exhibited.