Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Isomorphisms of lexicographic powers of the reals


Author: Salma Kuhlmann
Journal: Proc. Amer. Math. Soc. 123 (1995), 2657-2662
MSC: Primary 06A05; Secondary 04A20, 06F20
MathSciNet review: 1260172
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Abstract: Given a chain $ \Gamma $, we consider the lexicographic order $ {\mathbb{R}^\Gamma }$. If $ \Delta $ is a chain such that $ {\mathbb{R}^\Gamma } \simeq {\mathbb{R}^\Delta }$, we examine the question of whether necessarily $ \Gamma \simeq \Delta $. Under an additional hypothesis, we show that $ \Gamma $ and $ \Delta $ 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 $ \Gamma $ and $ \Delta $ are ordinals.


References [Enhancements On Off] (What's this?)

  • [FU] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1260172-4
Keywords: Lexicograhic products of the reals, order, ordinals, Archimedean complete groups
Article copyright: © Copyright 1995 American Mathematical Society