2 papers
math.LO2026
Sum-product Phenomenon Via Dimension
Yuyan He, Sergei Starchenko
We show a sum-product phenomenon in fields equipped with abstract dimension theories, which simultaneously generalizes the dimensions in geometric theories and Hrushovski's coarse…
math.LO2026
Combinatorics in one-based and related structures
Artem Chernikov, Sergei Starchenko
We consider some extremal combinatorial questions for bipartite graphs definable in stable one-based (and related) structures. We show that they satisfy both strong ErdÅs-Hajnal p…