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Preprint Number 1382

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1382. Gabriel Conant and Anand Pillay
Pseudofinite groups and VC-dimension
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Submission date: 9 February 2018

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 δ(x; y), we prove various aspects of “local fsg” for the right-stratified formula δ^r(x; y,u):=δ(x . u; y). This includes a δ^r-type-definable connected component, uniqueness of the pseudofinite counting measure as a left-invariant measure on δ^r-formulas, and generic compact domination for δ^r-definable sets.

Mathematics Subject Classification:

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Full text arXiv 1802.03361: pdf, ps.


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