Hahn’s Über die Nichtarchimedischen Grössensysteme and the Development of the Modern Theory of Magnitudes and Numbers to Measure Them

摘要: The ordered field ℜ of real numbers is course up to isomorphism the unique Dedekind continuous field. Equally important, though apparently less well known, fact that also Archimedean complete, idea an complete was introduced by Hans Hahn in his celebrated investigation Uber die nichtarchimedischen Grossensysteme which presented Royal Academy Sciences Vienna 1907. It a special case more general conception abelian group, motivated by, and substantially generalizes, as admits no proper extension field; is, satisfies Hilbert’s Axiom (arithmetic) Completeness (Hilbert 1900a, p. 183; 1903a, 16).