Representing ordinal numbers with arithmetically interesting sets of real numbers

Author: 

Dakota Blair, D
Hamkins, J
O’Bryant, K

Publication Date: 

1 January 2020

Journal: 

Integers

Last Updated: 

2021-01-30T06:23:45.713+00:00

Volume: 

20A

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

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article