标题： C₀(R)中不可数的素z-理想族 显示英文标题

标题： Uncountable families of prime z-ideals in C_0(R)

摘要： 记$\continuum=2^{\aleph_0}$为连续统的基数。 我们构造了一个有趣的族$(P_\alpha: \alpha\in\continuum)$的素$z$-理想在$\C_0(\reals)$中，具有以下性质： 如果$f\in P_{i_0}$对某个$i_0\in\continuum$，则$f\in P_i$对所有但有限个$i\in \continuum$； $\bigcap_{i\neq i_0} P_i \nsubset P_{i_0}$对每个$\i_0\in \continuum$。 我们还构建了一个序类型为$\kappa$的素$z$-理想在$\C_0(\reals)$中的良序递增链，以及一个良序递减链，对于任何基数为$\continuum$的序数$\kappa$。 显示英文摘要

摘要： Denote by $\continuum=2^{\aleph_0}$ the cardinal of continuum. We construct an intriguing family $(P_\alpha: \alpha\in\continuum)$ of prime $z$-ideals in $\C_0(\reals)$ with the following properties: If $f\in P_{i_0}$ for some $i_0\in\continuum$, then $f\in P_i$ for all but finitely many $i\in \continuum$; $\bigcap_{i\neq i_0} P_i \nsubset P_{i_0}$ for each $\i_0\in \continuum$. We also construct a well-ordered increasing chain, as well as a well-ordered decreasing chain, of order type $\kappa$ of prime $z$-ideals in $\C_0(\reals)$ for any ordinal $\kappa$ of cardinality $\continuum$.