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math.LO2026
Some results on NIP groups and their Ellis groups
Atticus Stonestrom
The paper develops a notion of piecewise (strong) f‑generic definable sets in NIP groups, shows they form an ideal, and uses this to obtain new results on the size and structure of…
math.LO2026
An arithmetic algebraic regularity lemma
Anand Pillay, Atticus Stonestrom
We give an 'arithmetic regularity lemma' for groups definable in finite fields, analogous to Tao's 'algebraic regularity lemma' for graphs definable in finite fields. More specific…
math.LO2025
On f-generic types in NIP groups
Atticus Stonestrom
`Definable amenability' of a definable group is the model-theoretic analogue of amenability of a discrete group; precisely, a definable group is said to be definably amenable if it…