Tiltan and Superclub
We show that one can force superclub with an arbitrarily large value of $\mathrm{cov}(\mathscr{M})$. We prove that the club principle is consistent with an arbitrarily large value of $\mathrm{add}(\mathscr{M})$. We also prove that if $\kappa $ is regular then superclub at $\kappa ^+$ implies $Q(\kap...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-07-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.434/ |
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| _version_ | 1825206215469170688 |
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| author | Garti, Shimon Shelah, Saharon |
| author_facet | Garti, Shimon Shelah, Saharon |
| author_sort | Garti, Shimon |
| collection | DOAJ |
| description | We show that one can force superclub with an arbitrarily large value of $\mathrm{cov}(\mathscr{M})$. We prove that the club principle is consistent with an arbitrarily large value of $\mathrm{add}(\mathscr{M})$. We also prove that if $\kappa $ is regular then superclub at $\kappa ^+$ implies $Q(\kappa ^+,\kappa ^+,\kappa ^+)$. |
| format | Article |
| id | doaj-art-2576890dca6b414ba0788db6b7495d27 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-2576890dca6b414ba0788db6b7495d272025-02-07T11:08:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-07-01361G585386110.5802/crmath.43410.5802/crmath.434Tiltan and SuperclubGarti, Shimon0Shelah, Saharon1Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, IsraelDepartment of Mathematics Rutgers University New Brunswick, NJ 08854, USA; EinsteinInstitute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, IsraelWe show that one can force superclub with an arbitrarily large value of $\mathrm{cov}(\mathscr{M})$. We prove that the club principle is consistent with an arbitrarily large value of $\mathrm{add}(\mathscr{M})$. We also prove that if $\kappa $ is regular then superclub at $\kappa ^+$ implies $Q(\kappa ^+,\kappa ^+,\kappa ^+)$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.434/Superclubclub (tiltan)invariants of measure and categoryinfinite graphssquare brackets |
| spellingShingle | Garti, Shimon Shelah, Saharon Tiltan and Superclub Comptes Rendus. Mathématique Superclub club (tiltan) invariants of measure and category infinite graphs square brackets |
| title | Tiltan and Superclub |
| title_full | Tiltan and Superclub |
| title_fullStr | Tiltan and Superclub |
| title_full_unstemmed | Tiltan and Superclub |
| title_short | Tiltan and Superclub |
| title_sort | tiltan and superclub |
| topic | Superclub club (tiltan) invariants of measure and category infinite graphs square brackets |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.434/ |
| work_keys_str_mv | AT gartishimon tiltanandsuperclub AT shelahsaharon tiltanandsuperclub |