A partial function f on an k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f . Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≥ 2 there exists a unique minim...

We develop a “motivic integration” version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and show (under some assumptions) that the Fourier transform of a conjugation-invariant test function does not depend on the form of the division algebra. This yields a motivi...

We show that type-definable subgroups of measure algebras are definable.

We show that if G is a stable group of finite weight with no infinite, infinite-index, chains of definable subgroups, then G is superstable of finite U rank. Combined with recent work of Palaćın and Sklinos, we conclude that (Z,+, 0) has no proper stable expansions of finite weight. A corollary of this result is that if P ⊆ Zn is definable in a finite dp-rank expansion of (Z,+, 0), and (Z,+, 0,...