Combinatorial Properties Related to the Higher Baumgartner's Axiom
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908905479602176 |
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| author | Krueger, John |
| author_facet | Krueger, John |
| contents | We isolate two combinatorial properties, each expressible by a $Π_2$-sentence over the structure $(H(ω_3),\in,ω_1,ω_2,\text{NS}_{ω_2})$, such that each property is consistent with CH, and their conjunction together with $2^ω\le ω_2$ and $2^{ω_1} = 2^{ω_2} = ω_3$ implies the existence of a c.c.c. forcing which forces the higher Baumgartner's axiom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20905 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorial Properties Related to the Higher Baumgartner's Axiom Krueger, John Logic Primary 03E05, 03E35, Secondary 03E40, 03E50 We isolate two combinatorial properties, each expressible by a $Π_2$-sentence over the structure $(H(ω_3),\in,ω_1,ω_2,\text{NS}_{ω_2})$, such that each property is consistent with CH, and their conjunction together with $2^ω\le ω_2$ and $2^{ω_1} = 2^{ω_2} = ω_3$ implies the existence of a c.c.c. forcing which forces the higher Baumgartner's axiom. |
| title | Combinatorial Properties Related to the Higher Baumgartner's Axiom |
| topic | Logic Primary 03E05, 03E35, Secondary 03E40, 03E50 |
| url | https://arxiv.org/abs/2603.20905 |