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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0450069-X
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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DOI: https://doi.org/10.1090/S0002-9939-1976-0450069-X
Article copyright: © Copyright 1976 American Mathematical Society