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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…
math.LO2026
Fractional Helly property and combinatorics of forking in NTP theories
Artem Chernikov, Chuyin Jiang
We investigate the class of FHP theories, i.e. theories of structures in which all definable families of sets satisfy the Fractional Helly Property (and its variants) from combinat…
math.LO2026
On n-distality, n-triviality and hypergraph regularity in NIP theories
Artem Chernikov, Francis Westhead
We study Keisler measures in strongly n-distal NIP theories, generalizing some results of Simon and Chernikov-Starchenko for distal theories and addressing some questions of Walker…