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arXiv · 2305.12509

Concerning Keisler Measures over ultraproducts

Kyle Gannon
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Abstract

As consequence of the VC theorem, any pseudo-finite measure over an NIP ultraproduct is generically stable. We demonstrate a converse of this theorem and prove that any finitely approximable measure over an ultraproduct is itself pseudo-finite (even without the NIP assumption). We also analyze the connection between the Morley product and the pseudo-finite product. In particular, we show that if $μ$ is definable and both $μ$ and $ν$ are pseudo-finite, then the Morley product of $μ$ and $ν$ agrees with the pseudo-finite product of $μ$ and $ν$. Using this observation, we construct generically stable idempotent measures on pseudo-finite NIP groups.

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Kyle Gannon. 2024-07-05. Concerning Keisler Measures over ultraproducts. https://arxiv.org/abs/2305.12509

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