论文标题
部分可观测时空混沌系统的无模型预测
A note on infinite partitions of free products of Boolean algebras
论文作者
论文摘要
如果$ a $是无限的布尔代数，则红衣主教不变$ \ mathfrak {a}（a）$被定义为无限分区的最小尺寸。红衣主教$ \ Mathfrak {a}（a \ oplus b）$，其中$ a \ oplus b $是布尔代数$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a和$ b $（其双重拓扑空间是$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a} $ \ nath $ a} $ a} $ {平等$ \ mathfrak {a}（a \ oplus b）= \ min \ lbrace \ mathfrak {a}（a），\ mathfrak {a}（a}（b）\ rbrace $尚不为所有infinite boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolean boolan boolean boolan boolean bool a $ a $ a $ a $ a $ a $ a $ b $。这里提供了$ \ mathfrak {a}（a \ oplus b）$的一些下限。
If $A$ is an infinite Boolean algebra the cardinal invariant $\mathfrak{a}(A)$ is defined as the smallest size of an infinite partition of $A$. The cardinal $\mathfrak{a}(A\oplus B)$, where $A\oplus B$ is the free product of the Boolean algebras $A$ and $B$ (whose dual topological space is the product of the dual topological spaces of $A$ and $B$), is below both $\mathfrak{a}(A)$ and $\mathfrak{a}(B)$. The equality $\mathfrak{a}(A\oplus B)=\min\lbrace\mathfrak{a}(A),\mathfrak{a}(B)\rbrace$ is not known to hold for all infinite Boolean algebras $A$ and $B$. Here some lower bounds of $\mathfrak{a}(A\oplus B)$ are provided.
