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Proceedings of the American Mathematical Society

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

 

 

Exponentiation of reals: effects of base choice


Author: R. Gurevič
Journal: Proc. Amer. Math. Soc. 99 (1987), 155-162
MSC: Primary 03E20; Secondary 04A99, 26A18
MathSciNet review: 866446
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Abstract: Let $ r > 1$ and $ {X_r}$ be the minimal set of reals containing 1 and closed under $ {\exp_r}:x \mapsto {r^x}$ and addition. The behavior of $ {X_r}$ is studied. In particular among possible order types of $ {X_r}$ there are $ \omega,{\omega ^\omega},\omega + q,\omega + 1 + q$, where $ q$ is the dense countable order without endpoints.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0866446-6
Keywords: Cantor derivative, perfect set, one-parameter iteration subgroup of the diffeomorphisms group
Article copyright: © Copyright 1987 American Mathematical Society