Epic math battle of history: Grothendieck vs Nikodym
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910720041418752 |
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| author | Głodkowski, Damian Widz, Agnieszka |
| author_facet | Głodkowski, Damian Widz, Agnieszka |
| contents | We define a $σ$-centered notion of forcing that forces the existence of a Boolean algebra with the Grothendieck property and without the Nikodym property. In particular the existence of such an algebra is consistent with the negation of the continuum hypothesis. The algebra we construct consists of Borel subsets of the Cantor set and has cardinality $ω_1$. We also show how to apply our method to streamline Talagrand's construction of such an algebra under the continuum hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Epic math battle of history: Grothendieck vs Nikodym Głodkowski, Damian Widz, Agnieszka Functional Analysis General Topology Logic 03E35, 03E75, 06E15, 28A33, 46E15, 46E27 We define a $σ$-centered notion of forcing that forces the existence of a Boolean algebra with the Grothendieck property and without the Nikodym property. In particular the existence of such an algebra is consistent with the negation of the continuum hypothesis. The algebra we construct consists of Borel subsets of the Cantor set and has cardinality $ω_1$. We also show how to apply our method to streamline Talagrand's construction of such an algebra under the continuum hypothesis. |
| title | Epic math battle of history: Grothendieck vs Nikodym |
| topic | Functional Analysis General Topology Logic 03E35, 03E75, 06E15, 28A33, 46E15, 46E27 |
| url | https://arxiv.org/abs/2401.13145 |