论文标题
单调正态性和Nabla产品
Monotone Normality and Nabla-Products
论文作者
论文摘要
Roitman的组合原理$δ$等效于Nabla产品的单调正态性，$ \ nabla（ω+1）^ω$。如果$ \ {x_n：nω\} $是一个可Metrizable空间的家族，而$ \ nabla_n x_n $是单调的，那么$ \ nabla_n x_n $是遗传性的。因此，如果$δ$保留，则盒子产品$ \ square（ω+1）^ω$是paracompact。 $δ$的大片段保留在$ \ mathsf {zfc} $中，产生$ \ nabla（ω+1）^ω$的大子空间，它们在单调上是正常的。可数的可数nabla产品分别是：$ \ le \ le \ mathfrak {c} $或可分开的任意：$ \ mathfrak {b} = \ mathfrak {d} $，$ \ mathfrak {d} $，$ \ mathfrak {d} = \ mathfrak} $ opthfrak，分别是单调的。 $ \ nabla a（ω_1）^ω$和$ \ nabla（ω_1+1）^ω$是一致和独立的。在$ \ Mathsf {Zfc} $中，$ \ nabla a（ω_2）^ω$也不是$ \ nabla（ω_2+1）^ω$是正常的。
Roitman's combinatorial principle $Δ$ is equivalent to monotone normality of the nabla product, $\nabla (ω+1)^ω$. If $\{ X_n : n\in ω\}$ is a family of metrizable spaces and $\nabla_n X_n$ is monotonically normal, then $\nabla_n X_n$ is hereditarily paracompact. Hence, if $Δ$ holds then the box product $\square (ω+1)^ω$ is paracompact. Large fragments of $Δ$ hold in $\mathsf{ZFC}$, yielding large subspaces of $\nabla (ω+1)^ω$ that are `really' monotonically normal. Countable nabla products of metrizable spaces which are respectively: arbitrary, of size $\le \mathfrak{c}$, or separable, are monotonically normal under respectively: $\mathfrak{b}=\mathfrak{d}$, $\mathfrak{d}=\mathfrak{c}$ or the Model Hypothesis. It is consistent and independent that $\nabla A(ω_1)^ω$ and $\nabla (ω_1+1)^ω$ are hereditarily normal (or hereditarily paracompact, or monotonically normal). In $\mathsf{ZFC}$ neither $\nabla A(ω_2)^ω$ nor $\nabla (ω_2+1)^ω$ is hereditarily normal.
