Infinite-Exponent Partition Relations on Higher Analogues of the Real Line
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909008077520896 |
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| author | Gardiner, Lyra A. Schilhan, Jonathan Weinert, Thilo |
| author_facet | Gardiner, Lyra A. Schilhan, Jonathan Weinert, Thilo |
| contents | We present a number of results concerning infinite-exponent partition relations on linear orders of the form $\langle {}^α2,<_{\text{lex}}\rangle$ for $α$ an ordinal, generalising the setting of the real line, working throughout in ZF without the Axiom of Choice. As a particular consequence of our results, we obtain a full classification of the relation $\langle {}^α2,<_{\text{lex}}\rangle \rightarrow (τ)^τ$ for $τ$ countable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00636 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinite-Exponent Partition Relations on Higher Analogues of the Real Line Gardiner, Lyra A. Schilhan, Jonathan Weinert, Thilo Logic Combinatorics Primary 03E02, Secondary 06A05, 03E25, 05D10 We present a number of results concerning infinite-exponent partition relations on linear orders of the form $\langle {}^α2,<_{\text{lex}}\rangle$ for $α$ an ordinal, generalising the setting of the real line, working throughout in ZF without the Axiom of Choice. As a particular consequence of our results, we obtain a full classification of the relation $\langle {}^α2,<_{\text{lex}}\rangle \rightarrow (τ)^τ$ for $τ$ countable. |
| title | Infinite-Exponent Partition Relations on Higher Analogues of the Real Line |
| topic | Logic Combinatorics Primary 03E02, Secondary 06A05, 03E25, 05D10 |
| url | https://arxiv.org/abs/2605.00636 |