7 papers
Some results on NIP groups and their Ellis groups
Atticus Stonestrom
This paper has several parts. We begin by developing a theory of `piecewise (strong) f-genericity' in NIP groups, where we call a definable set piecewise (strong) f-generic if some…
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…
On non-abelian dp-minimal groups I: the torsion-free and distal cases
Atticus Stonestrom
We give some results on dp-minimal groups. First we show that any torsion-free dp-minimal group is abelian; along the way show that any dp-minimal group admitting a principal f-gen…
Forking and invariant measures in NIP theories
Anand Pillay, Atticus Stonestrom
We give an example of an NIP theory in which there is a formula that does not fork over but has measure under any global -invariant Keisler measu…
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…
Product-free sets in approximate subgroups of distal groups
Atticus Stonestrom
Recall that a subset of a group is 'product-free' if , ie if for all . Let be a group definable in a distal structure. We…
Some model theory of
Atticus Stonestrom
'Skolem arithmetic' is the complete theory of the multiplicative monoid . We give a full characterization of the -definable stably embedded set…