关于理想$(v^0)$
On the ideal $(v^0)$
摘要：
$σ$ -理想的$(v^0)$与银强迫有关，参见\cite{bre}。此外，它构成了所有完全环形空集的家族，参见\cite{hal}。我们引入段和$*$ -段拓扑，以说明$(v^0)$与拉姆齐空集族的一些相似之处。为了描述$add(v^0)$，我们采用了一个基矩阵引理的证明。结果也是一致的。在$t= \min \{\cf (\frak c), r\} $假设下证实了Halbeisen的猜想$cov(v^0) = add(v^0)$.假设$h=ω_1$意味着$(v^0)$具有理想型$(\frak c, ω_1,\frak c)$。
英文摘要：
The $σ$-ideal $(v^0)$ is associated with the Silver forcing, see \cite{bre}. Also, it constitutes the family of all completely doughnut null sets, see \cite{hal}. We introduce segments and $*$-segments topologies, to state some resemblances of $(v^0)$ to the family of Ramsey null sets. To describe $add(v^0)$ we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen's conjecture $cov(v^0) = add(v^0)$ is confirmed under the hypothesis $t= \min \{\cf (\frak c), r\} $. The hypothesis $h=ω_1$ implies that $(v^0)$ has the ideal type $(\frak c, ω_1,\frak c)$.
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