拓扑柱形代数中的归并、插值和同余扩张性质
Amalgamation, interpolation and congruence extension properties in topological cylindric algebras
摘要：
维数为α，α为任意序数的拓扑柱形代数代数是维数为α的柱形代数代数，它用αS4模态展开.可表示代数中的S4模态是由基于其圆柱约简的表示的拓扑导出的，这不一定是Alexandrov拓扑。对于α>2，可表示代数类是一个不能用有限模式公理化的簇，事实上，Andreka证明了所有复杂性都是关于柱形代数的表示的结果（关于公理化所需变量的数量）（关于Sahlqvist公理化和正则性）和其他，转移到拓扑加法，通过实现一个非常简单的“离散拓扑化一个柱形代数”的过程给定一个维度为α的柱形代数，可以在α中添加许多内部单位元运算，后一个代数可表示为拓扑柱形代数当且仅当前一个是由离散拓扑导出的表示。本文研究了各种拓扑柱形代数的合并性质。我们恢复，在拓扑的背景下，所有的结果证明了安德烈卡，角Madarasz，Nemeti，Pigozzi，塞恩，赛义德艾哈迈德，萨吉，Shelah，西蒙，和其他柱形代数和更多。
英文摘要：
Topological cylindric algebras of dimension α, αany ordinal are cylindric algebras with dimension αexpanded with αS4 modalities. The S4 modalities in representable algebras are induced by a topology on the base of the representation of its cylindric reduct, that is not necessarily an Alexandrov topolgy. For α>2, the class of representable algebras is a variety that is not axiomatized by a finite schema, and in fact all complexity results on representations for cylindric algebras, proved by Andreka (concerning number of variables needed for axiomatizations) Hodkinson (on Sahlqvist axiomatizations and canonicity) and others, transfer to the topological addition, by implementing a very simple procedure of `discretely topologizing a cylindric algebra' Given a cylindric algebra of dimension α, one adds αmany interior identity operations, the latter algebra is representable as a topological cylindric algebra if and only if the former is; the representation induced by the discrete topology. In this paper we investigate amalgamation properties for various classes of topological cylindric algebras of all dimensions. We recover, in the topological context, all of the results proved by Andreka, Comer Madarasz, Nemeti, Pigozzi, Sain, Sayed Ahmed, Sagi, Shelah, Simon, and others for cylindric algebras and much more.
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