C_0（R）中素z-理想的不可数族
Uncountable families of prime z-ideals in C_0(R)
摘要：
用$\continuum=2^{\aleph_0}$表示连续统的基数。我们构造了一个有趣的家庭$(P_α: α\in\continuum)$素$z$理想在$\C_0(\reals)$具有以下性质：如果$f\in P_{i_0}$的一些$i_0\in\continuum$，那么$f\in P_i$的所有，但许多$i\in \continuum$ ; $\bigcap_{i\neq i_0} P_i \nsubset P_{i_0}$的每个$ı_0\in \continuum$。对于基数为$\continuum$的任意序数$κ$，我们还构造了$\C_0(\reals)$中素$z$ -理想的序型$κ$的良序增链和良序减链.
英文摘要：
Denote by $\continuum=2^{\aleph_0}$ the cardinal of continuum. We construct an intriguing family $(P_α: α\in\continuum)$ 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 $ı_0\in \continuum$. We also construct a well-ordered increasing chain, as well as a well-ordered decreasing chain, of order type $κ$ of prime $z$-ideals in $\C_0(\reals)$ for any ordinal $κ$ of cardinality $\continuum$.
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