a1 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA, E-mail: firstname.lastname@example.org
a2 Mathematical Institute, University of Oxford, 24–29 St. Giles, Oxford OX1 3LB, UK, E-mail: email@example.com
We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.
(Received February 04 2002)
(Revised October 21 2002)