论文标题
通过拓扑和紧张圆柱代数的空间和时间
Space and time via Topological and Tense cylindric algebras
论文作者
论文摘要
令$α$为arbritary序列，$ 2 <n <ω$。在\ cite {3}中被接受在Quaestiones Mathaticae中的出版物中，我们使用代数逻辑，插值，使用$α$ a $的拓扑逻辑变量与$α$许多变量进行了简短的$ \ sftopl_α$。这是\ cite {3}的续集;模态圆柱代数的第二部分，我们研究$ \ sftopl_α$的代数其他特性。模态圆柱代数是无限尺寸的圆柱代数，并通过单元模态扩展，从单峰逻辑$ \ sf l $（例如$ \ sf k5 $或$ \ sf s4 $）继承其语义。使用代数逻辑的方法，我们在符号$ \ sftca_α$中研究拓扑（当$ \ sf l = s4 $）。我们研究完整性和省略类型$ \ sf ott $ s $ \ sftopl_Ω$和$ \ sftenl_Ω$，通过证明为本地有限的此类代数证明了几种可用性结果。此外，我们研究了$ {\ sf tca} _ {n} $和$ {\ sf tenl} _n $的原子 - 官方性概念，在模态逻辑中是一种众所周知的持久性属性，涉及$ \ sf ott $ for $ {\ sf ott $ for $ {\ sf topl topl} $ _n $和$ sf。我们研究拓扑圆柱代数的代表性，省略类型，插值和复杂性ISS（例如不可证明性）。在本文的续集中，我们介绍了时间循环代数，并指出了如何将空间（拓扑代数）和时间（时间代数）代数合并为代数的方式（颞代代数）形成拓扑 - 周期性的圆柱代数，这些代数将自己包含空间空间时空的gemetime gemetries，in pul alge alge alge alge algebraicy yourbraic and ofbraic and ang braicy yourbraicy yourbraicy yourbraic yourbraicy y。
Let $α$ be an arbritary ordinal, and $2<n<ω$. In \cite{3} accepted for publication in Quaestiones Mathematicae, we studied using algebraic logic, interpolation, amalgamation using $α$ many variables for topological logic with $α$ many variables briefly $\sf TopL_α$. This is a sequel to \cite{3}; the second part on modal cylindric algebras, where we study algebraically other properties of $\sf TopL_α$. Modal cylindric algebras are cylindric algebras of infinite dimension expanded with unary modalities inheriting their semantics from a unimodal logic $\sf L$ such as $\sf K5$ or $\sf S4$. Using the methodology of algebraic logic, we study topological (when $\sf L=S4$), in symbols $\sf TCA_α$. We study completeness and omitting types $\sf OTT$s for $\sf TopL_ω$ and $\sf TenL_ω$, by proving several representability results for locally finite such algebras. Furthermore, we study the notion of atom-canonicity for both ${\sf TCA}_{n}$ and ${\sf TenL}_n$, a well known persistence property in modal logic, in connection to $\sf OTT$ for ${\sf TopL}_n$ and ${\sf TeLCA}_n$, respectively. We study representability, omitting types, interpolation and complexity isssues (such as undecidability) for topological cylindric algebras. In a sequel to this paper, we introduce temporal cyindric algebras and point out the way how to amalgamate algebras of space (topological algebars) and algebras of time (temporal algebras) forming topological-temporal cylindric algebras that lend themselves to encompassing spacetime gemetries, in a purely algebraic manner.
