Reaping Numbers of Boolean Algebras
| dc.creator | Dow, A. | |
| dc.creator | Steprāns, J | |
| dc.creator | Watson, W. S. | |
| dc.date | 1992-04-23 | |
| dc.date.accessioned | 2026-07-07T09:14:45Z | |
| dc.date.available | 2026-07-07T09:14:45Z | |
| dc.description | A subset $A$ of a Boolean algebra $B$ is said to be $(n,m)$-reaped if there is a partition of unity $P \subset B$ of size $n$ such that the cardinality of $\{b \in P: b \wedge a \neq \emptyset\}$ is greater than or equal to $m$ for all $a\in A$. The reaping number $r_{n,m}(B)$ of a Boolean algebra $B$ is the minimum cardinality of a set $A \subset B\setminus \{0\}$ such which cannot be $(n,m)$-reaped. It is shown that, for each $n \in ω$, there is a Boolean algebra $B$ such that $r_{n+1,2}(B) \neq r_{n,2}(B)$. Also, $\{r_{n,m}(B) : \{n,m\}\subseteqω\}$ consists of at most two consecutive integers. The existence of a Boolean algebra $B$ such that $r_{n,m}(B) \neq r_{n',m'}(B)$ is equivalent to a statement in finite combinatorics which is also discussed. | |
| dc.identifier | https://arxiv.org/abs/math/9204210 | |
| dc.identifier | http://arxiv.org/abs/math/9204210 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152790 | |
| dc.subject | Logic | |
| dc.title | Reaping Numbers of Boolean Algebras | |
| dc.type | text |