| Autor: |
Machura, Michał, Shelah, Saharon, Tsaban, Boaz |
| Rok vydání: |
2014 |
| Předmět: |
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| Zdroj: |
Fundamenta Mathematicae 234 (2016), 15-40 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.4064/fm124-8-2015 |
| Popis: |
The \emph{linear refinement number} $\mathfrak{lr}$ is the minimal cardinality of a centered family in $[\omega]^\omega$ such that no linearly ordered set in $([\omega]^\omega,\subseteq^*)$ refines this family. The \emph{linear excluded middle number} $\mathfrak{lx}$ is a variation of $\mathfrak{lr}$. We show that these numbers estimate the critical cardinalities of a number of selective covering properties. We compare these numbers to the classic combinatorial cardinal characteristics of the continuum. We prove that $\mathfrak{lr}=\mathfrak{lx}=\mathfrak{fd}$ in all models where the continuum is at most $\aleph_2$, and that the cofinality of $\mathfrak{lr}$ is uncountable. Using the method of forcing, we show that $\mathfrak{lr}$ and $\mathfrak{lx}$ are not provably equal to $\mathfrak{d}$, and rule out several potential bounds on these numbers. Our results solve a number of open problems. |
| Databáze: |
arXiv |
| Externí odkaz: |
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