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We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only"quantifier elimination relative to ordered sets"in the… (More)

For oscillatory functions on local fields coming from motivic exponential functions, we show that integrability over $Q_p^n$ implies integrability over $F_p ((t))^n$ for large $p$, and vice versa.… (More)

It was already known that a p-adic, locally Lipschitz continuous semialgebraic function is piecewise Lipschitz continuous, where the pieces can be taken semi-algebraic. We prove that if the function… (More)

Consider multisets A in the group G = (Z/nZ) such that no non-empty subset has sum zero. It is known for long that the maximal cardinality of such a set is 2n − 2, and there is a conjecture of Gao… (More)

- Luck Darnière, Immanuel Halupczok
- J. Symb. Log.
- 2017

We prove that for p-optimal fields (a very large subclass of p-minimal fields containing all the known examples) a cell decomposition theorem follows from methods going back to Denef’s paper [Den84].… (More)

We propose to grok Lipschitz stratifications from a non-arch imedean point of view and thereby show that they exist for closed definable sets in any power-bo undedo-minimal structure on a real closed… (More)

We define"t-stratifications", a strong notion of stratifications for Henselian valued fields $K$ of equi-characteristic 0, and prove that they exist. In contrast to classical stratifications in… (More)

Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.

Let G be a connected reductive algebraic group over a nonArchimedean local field K, and let g be its Lie algebra. By a theorem of Harish-Chandra, if K has characteristic zero, the Fourier transforms… (More)