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Proceedings of the American Mathematical Society

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



Analysis of an exponential equation with ordinal variables

Author: J. L. Hickman
Journal: Proc. Amer. Math. Soc. 61 (1976), 105-111
MSC: Primary 04A10
MathSciNet review: 0450069
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Abstract: This paper is concerned with the analysis of the equation $ {x^y} = {y^z}$, where $ x,y,z$ are variables ranging over ordinals, and where both sides of the equation are transfinite in value. The method used for this analysis consists in regarding $ y$ as a parameter and $ x$ as an independent variable, and determining necessary and sufficient conditions to be placed upon $ x$ so that the resulting equation in $ z$ has a solution. Extensive use is made of normal form, as well as results in ordinal arithmetic by both Bachmann and Sherman.

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Article copyright: © Copyright 1976 American Mathematical Society