Dependent measures in independent theories
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915328945029120 |
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| author | Khanaki, Karim |
| author_facet | Khanaki, Karim |
| contents | We introduce the notion of dependence, as a property of a Keisler measure, and generalize several results of [HPS13] on generically stable measures (in $NIP$ theories) to arbitrary theories. Among other things, we show that this notion is very natural and fundamental for several reasons: (i) all measures in $NIP$ theories are dependent, (ii) all types and all $fim$ measures in any theory are dependent, and (iii) as a crucial result in measure theory, the Glivenko-Cantelli class of functions (formulas) is characterized by dependent measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_11973 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dependent measures in independent theories Khanaki, Karim Logic We introduce the notion of dependence, as a property of a Keisler measure, and generalize several results of [HPS13] on generically stable measures (in $NIP$ theories) to arbitrary theories. Among other things, we show that this notion is very natural and fundamental for several reasons: (i) all measures in $NIP$ theories are dependent, (ii) all types and all $fim$ measures in any theory are dependent, and (iii) as a crucial result in measure theory, the Glivenko-Cantelli class of functions (formulas) is characterized by dependent measures. |
| title | Dependent measures in independent theories |
| topic | Logic |
| url | https://arxiv.org/abs/2109.11973 |