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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.23340 |
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| _version_ | 1866915820584566784 |
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| author | Dialiatsis, Spyridon Khomskii, Yurii |
| author_facet | Dialiatsis, Spyridon Khomskii, Yurii |
| contents | The Raisonnier Filter is a combinatorial object isolated by Jean Raisonnier in order to simplify Shelah's proof that if all $\boldsymbolΣ^1_3$ sets are Lebesgue-measurable then there is an inner model with an inaccessible cardinal. In this paper, we study the combinatorics of a general version of the Raisonnier filter, with an eye to potential applications in descriptive set theory. Among the most interesting of our results is a partial converse to Raisonnier's theorem, which can be used to provide a new characterisation of the statement "all $\boldsymbolΣ^1_2$ sets are measurable". We also introduce an ideal on the Cantor Space induced by the Raisonnier filter and study its cardinal characteristics, connecting them to the well-known characteristics in Cichoń's Diagram. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23340 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorial Properties of the Raisonnier Filter Dialiatsis, Spyridon Khomskii, Yurii Logic The Raisonnier Filter is a combinatorial object isolated by Jean Raisonnier in order to simplify Shelah's proof that if all $\boldsymbolΣ^1_3$ sets are Lebesgue-measurable then there is an inner model with an inaccessible cardinal. In this paper, we study the combinatorics of a general version of the Raisonnier filter, with an eye to potential applications in descriptive set theory. Among the most interesting of our results is a partial converse to Raisonnier's theorem, which can be used to provide a new characterisation of the statement "all $\boldsymbolΣ^1_2$ sets are measurable". We also introduce an ideal on the Cantor Space induced by the Raisonnier filter and study its cardinal characteristics, connecting them to the well-known characteristics in Cichoń's Diagram. |
| title | Combinatorial Properties of the Raisonnier Filter |
| topic | Logic |
| url | https://arxiv.org/abs/2602.23340 |