自由积中没有正则的正锥
No positive cone in a free product is regular
摘要：
我们证明了两个非平凡的、可生成的左序群的自由积上不存在左序，使得相应的正锥由正则语言表示。由于有秩序的自由群的秩至少为2的正锥语言是上下文无关的（事实上，1-计数器语言），我们的结果提供了一个约束的语言复杂性的正锥在自由积，这是最好的可能在乔姆斯基层次。它还提供了一个加强的结果克里斯托瓦尔里瓦斯指出，正锥的自由积的非平凡，非线性生成，左序群不能非线性生成作为一个半群。
英文摘要：
We show that there exists no left order on the free product of two nontrivial, finitely generated, left-orderable groups such that the corresponding positive cone is represented by a regular language. Since there are orders on free groups of rank at least two with positive cone languages that are context-free (in fact, 1-counter languages), our result provides a bound on the language complexity of positive cones in free products that is the best possible within the Chomsky hierarchy. It also provides a strengthening of a result by Cristobal Rivas stating that the positive cone in a free product of nontrivial, finitely generated, left-orderable groups cannot be finitely generated as a semigroup.
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