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Preprint Number 2268
2268. Christian Schulz Undefinability of multiplication in Presburger arithmetic with sets of
powers E-mail: Submission date: 23 September Abstract: We begin by proving that any Presburger-definable image of one or more sets of powers has zero natural density. Then, by adapting the proof of a dichotomy result on o-minimal structures by Friedman and Miller, we produce a similar dichotomy for expansions of Presburger arithmetic on the integers. Combining these two results, we obtain that the expansion of the ordered group of integers by any number of sets of powers does not define multiplication. Mathematics Subject Classification: Keywords and phrases: |

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