由完备化生成的簇
Varieties generated by completions
AI总结：
本文证明有序判别簇中完备化不生成持续有限代数，有限可测关系代数均为持续有限，据此否定回答Maddux的问题1.1(1)，证实Frias-Maddux的有限极大关系代数不在目标簇中，并指出两簇间存在连续统多个簇。
摘要：
我们证明，在任何有序判别簇中，持续有限代数不会由代数的完备化生成。持续有限代数是指没有无限单扩张的代数。我们证明所有有限可测关系代数都是持续有限的。这些定理的一个应用是，由可表示关系代数的完备化生成的簇不包含所有关系代数。这否定回答了R. Maddux一篇论文中的问题1.1(1)。同时，我们证实了该论文中的一个建议，即M. Frias和R. Maddux联合论文中构造的有限极大关系代数不在由可表示关系代数的完备化生成的簇中。我们证明，在由可表示关系代数的完备化生成的簇与关系代数的簇之间存在连续统多个簇。
英文摘要：
We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation algebras are all persistently finite. An application of these theorems is that the variety generated by the completions of representable relation algebras does not contain all relation algebras. This answers Problem 1.1(1) from a paper by R. Maddux in the negative. At the same time, we confirm the suggestion in that paper that the finite maximal relation algebras constructed in a joint paper by M. Frias and R. Maddux are not in the variety generated by the completions of representable relation algebras. We prove that there are continuum many varieties between the variety generated by the completions of representable relation algebras and the variety of relation algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
