Isomorphisms of lexicographic powers of the reals
Abstract: Given a chain , we consider the lexicographic order . If is a chain such that , we examine the question of whether necessarily . Under an additional hypothesis, we show that and will have the same order types of well ordered subsets. Among other things, this yields an affirmative answer to the above question in the case where and are ordinals.
Keywords: Lexicograhic products of the reals, order, ordinals, Archimedean complete groups
Article copyright: © Copyright 1995 American Mathematical Society