论文标题
随机模型有一个p测量
There is a P-measure in the random model
论文作者
论文摘要
我们说，如果$ω$上的有限添加概率度量$ $ $ $ $是\ emph {a p-measure}，如果它在点上消失，并且对于$ e \ e \subseteqΩ$ $ e \ subseteq $ $ e \ sebSeteeq^* e_n $的$ e \ subseteq的无限子集$ e \ subseteq $ and $ n $ and $ n $ and = \ lim_ {n \ to \ infty}μ（e_n）$。因此，p测量以自然的p点概括，众所周知，与p点相似，它们的存在与$ \ mathsf {zfc} $独立。在本文中，我们表明，通过将任意数量的随机REAL添加到$ \ Mathsf {Ch} $的模型中获得了p量。作为推论，我们在经典的随机模型$ω^*$中获得的，其中包含一个无处密集的CCC封闭p-stet。
We say that a finitely additive probability measure $μ$ on $ω$ is \emph{a P-measure} if it vanishes on points and for each decreasing sequence $(E_n)$ of infinite subsets of $ω$ there is $E\subseteqω$ such that $E\subseteq^* E_n$ for each $n\inω$ and $μ(E) = \lim_{n\to\infty}μ(E_n)$. Thus, P-measures generalize in a natural way P-points and it is known that, similarly as in the case of P-points, their existence is independent of $\mathsf{ZFC}$. In this paper we show that there is a P-measure in the model obtained by adding any number of random reals to a model of $\mathsf{CH}$. As a corollary, we obtain that in the classical random model $ω^*$ contains a nowhere dense ccc closed P-set.
