Exponentiation of reals: effects of base choice
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- by R. Gurevič PDF
- Proc. Amer. Math. Soc. 99 (1987), 155-162 Request permission
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.References
- R. Gurevič, Exponentiation of reals: effects of base choice, Proc. Amer. Math. Soc. 99 (1987), no. 1, 155–162. MR 866446, DOI 10.1090/S0002-9939-1987-0866446-6
- K. Kuratowski and A. Mostowski, Set theory, PWN—Polish Scientific Publishers, Warsaw; North-Holland Publishing Co., Amsterdam, 1968. Translated from the Polish by M. Maczyński. MR 0229526
- Hilbert Levitz, The Cartesian product of sets and the Hessenberg natural product of ordinals, Czechoslovak Math. J. 29(104) (1979), no. 3, 353–358. MR 536062, DOI 10.21136/CMJ.1979.101618
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 155-162
- MSC: Primary 03E20; Secondary 04A99, 26A18
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866446-6
- MathSciNet review: 866446