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arXiv · 1802.03361

Pseudofinite groups and VC-dimension

Gabriel Conant·Anand Pillay
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Abstract

We develop local NIP group theory in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure $G$ expanding a group, and left invariant NIP formula $\delta(x;\bar{y})$, we prove various aspects of "local fsg" for the right-stratified formula $\delta^r(x;\bar{y},u):=\delta(x\cdot u;\bar{y})$. This includes a $\delta^r$-type-definable connected component, uniqueness of the pseudofinite counting measure as a left-invariant measure on $\delta^r$-formulas, and generic compact domination for $\delta^r$-definable sets.

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Gabriel Conant, Anand Pillay. 2018-02-09. Pseudofinite groups and VC-dimension. https://arxiv.org/abs/1802.03361

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