论文标题
代表关系代数的一阶公理需要无限的量词深度公式
First-order axiomatisations of representable relation algebras need formulas of unbounded quantifier depth
论文作者
论文摘要
使用彩虹结构和各种卵石和着色游戏的变体，我们证明RRA（所有代表关系代数的类别）不能通过任何界限量化器深度的一阶关系代数理论来公理化。我们还证明，在（RRA）的类中，ATOM结构的（RRA）代表性，原子关系代数无法通过仅使用有限数量变量数量的RA原子结构语言中的任何一组句子来定义。
Using a variation of the rainbow construction and various pebble and colouring games, we prove that RRA, the class of all representable relation algebras, cannot be axiomatised by any first-order relation algebra theory of bounded quantifier depth. We also prove that the class At(RRA) of atom structures of representable, atomic relation algebras cannot be defined by any set of sentences in the language of RA atom structures that uses only a finite number of variables.
