论文标题
某些遗传性不可回报的空间的模态逻辑
Modal Logics of Some Hereditarily Irresolvable Spaces
论文作者
论文摘要
A topological space is \emph{hereditarily $k$-irresolvable} if none of its subspaces can be partitioned into $k$ dense subsets, We use this notion to provide a topological semantics for a sequence of modal logics whose $n$-th member K4$\mathbb{C}_n$ is characterised by validity in transitive Kripke frames of circumference at most $n$.我们表明，在将模式$ \钻石$解释为派生的（限制点）操作的情况下，K4 $ \ mathbb {c} _n $在所有遗传性$ n+1 $ irresolvable的空间中都有有效性的特征，并且具有T $ _D $分离属性。 我们还确定当涉及的空间类别仅限于那些弱分散，拥挤或公开不可思议的k4 $ \ mathbb {c} _n $的扩展，后者意味着每个非空的开放子空间都是2个不可回复的。最后，我们给出了K4M的拓扑语义，其中M是McKinsey Axiom。
A topological space is \emph{hereditarily $k$-irresolvable} if none of its subspaces can be partitioned into $k$ dense subsets, We use this notion to provide a topological semantics for a sequence of modal logics whose $n$-th member K4$\mathbb{C}_n$ is characterised by validity in transitive Kripke frames of circumference at most $n$. We show that under the interpretation of the modality $\Diamond$ as the derived set (of limit points) operation, K4$\mathbb{C}_n$ is characterised by validity in all spaces that are hereditarily $n+1$-irresolvable and have the T$_D$ separation property. We also identify the extensions of K4$\mathbb{C}_n$ that result when the class of spaces involved is restricted to those that are weakly scattered, or crowded, or openly irresolvable, the latter meaning that every non-empty open subspace is 2-irresolvable. Finally we give a topological semantics for K4M, where M is the McKinsey axiom.
