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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Isomorphisms of lexicographic powers of the reals
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by Salma Kuhlmann
Proc. Amer. Math. Soc. 123 (1995), 2657-2662
DOI: https://doi.org/10.1090/S0002-9939-1995-1260172-4

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
  • 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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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 2657-2662
  • MSC: Primary 06A05; Secondary 04A20, 06F20
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1260172-4
  • MathSciNet review: 1260172