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

  • L. van den Dries (a1) and A. J. Wilkie (a2)
  • DOI:
  • Published online: 01 March 2014

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.

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[3]H. Groemer , On the extension of additive functionals on classes of convex sets, Pacific Journal of Mathematics, vol. 75 (1978), pp. 397410.

[4]L. Lipshitz , The diophantine problem for addition and divisibility, Transactions of the American Mathematical Society, vol. 235 (1978), pp. 271283.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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