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pro vyhledávání: '"Stonestrom, Atticus"'
Autor:
Pillay, Anand, Stonestrom, Atticus
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 specifically, we show that, for any $M>0$, any finite field $\mathbf{F}$, and
Externí odkaz:
http://arxiv.org/abs/2412.11206
Autor:
Stonestrom, Atticus
Let $G$ be a dp-minimal group; we prove some consequences of several different hypotheses on $G$. First, if $G$ is torsion-free, then it is abelian. Second, if $G$ admits a distal f-generic type, then it is virtually nilpotent; we prove this by equip
Externí odkaz:
http://arxiv.org/abs/2308.04209
Autor:
Pillay, Anand, Stonestrom, Atticus
We give an example of an NIP theory $T$ in which there is a formula that does not fork over $\varnothing$ but has measure $0$ under any global $\varnothing$-invariant Keisler measure, and we show that this cannot occur if $T$ is also first-order amen
Externí odkaz:
http://arxiv.org/abs/2307.11037
Autor:
Stonestrom, Atticus
Let $G$ be a group definable in an NIP theory. We prove that, if $G$ admits a global f-generic type, then $G$ is definably amenable, answering a question of Chernikov and Simon. As an application, we show that every dp-minimal group is definably amen
Externí odkaz:
http://arxiv.org/abs/2303.13470
Autor:
Stonestrom, Atticus
Recall that a subset $X$ of a group $G$ is 'product-free' if $X^2\cap X=\varnothing$, ie if $xy\notin X$ for all $x,y\in X$. Let $G$ be a group definable in a distal structure. We prove there are constants $c>0$ and $\delta\in(0,1)$ such that every f
Externí odkaz:
http://arxiv.org/abs/2208.10604
Autor:
Stonestrom, Atticus
'Skolem arithmetic' is the complete theory $T$ of the multiplicative monoid $(\mathbb{N},\cdot)$. We give a full characterization of the $\varnothing$-definable stably embedded sets of $T$, showing in particular that, up to the relation of having the
Externí odkaz:
http://arxiv.org/abs/2109.01131
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