The Journal of Symbolic Logic

Research Article

The laws of integer divisibility, and solution sets of linear divisibility conditions

L. van den Driesa1 and A. J. Wilkiea2

a1 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA, E-mail:

a2 Mathematical Institute, University of Oxford, 24–29 St. Giles, Oxford OX1 3LB, UK, E-mail:


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)