Article
| Title: | Two-cardinal splitting (English) |
| Author: | Hrušák, Michael |
| Author: | Castro, Yhon J. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 66 |
| Issue: | 1 |
| Year: | 2025 |
| Pages: | 81-86 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We introduce and study a version of the classical splitting numbers $\mathfrak{s}(\kappa)$ with two parameters $\kappa\leq\lambda$ denoted by $\mathfrak{s}(\kappa,\lambda)$ and defined as the minimal size of a family $\mathcal S$ of subsets of $\lambda$ such that for every subset $A$ of $\lambda$ of size $\kappa$ there is an $S\in\mathcal S$ such that $|A\cap S|=|A\setminus S|=\kappa$. We focus on the cases when $\kappa=\mu^+$ and $\lambda=\mu^{++}$. We give several results that only depend on cardinal arithmetic, in particular, on the value that $2^{\kappa}$ assumes. (English) |
| Keyword: | two cardinal splitting |
| MSC: | 03E05 |
| MSC: | 03E10 |
| MSC: | 03E17 |
| DOI: | 10.14712/1213-7243.2025.015 |
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| Date available: | 2026-05-15T05:56:57Z |
| Last updated: | 2026-05-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153613 |
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