Author
Dakota Blair, D
Hamkins, J
O’Bryant, K
Journal title
Integers
Volume
20A
Last updated
2021-10-19T13:24:04.47+01:00
Page
1-9
Abstract
© 2020, Colgate University. All rights reserved. For a real number x and set of natural numbers A, define x * A:= {xa mod 1: A ϵ A} ⊆ (0, 1). We consider relationships between x, A, and the order-type of x * A. For example, for every irrational x and countable order-type ↵, there is an A with x * A⁓α, but if ↵ is a well order, then A must be a thin set. If, however, A is restricted to be a subset of the powers of 2, then not every order type is possible, although arbitrarily large countable well orders arise.
Symplectic ID
1147269
Publication type
Journal Article
Publication date
1 January 2020
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