Concerning Keisler Measures over ultraproducts
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917713151000576 |
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| author | Gannon, Kyle |
| author_facet | Gannon, Kyle |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12509 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Concerning Keisler Measures over ultraproducts Gannon, Kyle Logic 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. |
| title | Concerning Keisler Measures over ultraproducts |
| topic | Logic |
| url | https://arxiv.org/abs/2305.12509 |