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
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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
- 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
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