字问题和小题
Word problems and ceers
摘要：
本文讨论的问题是，哪些ceer可以通过可计算的可计算的（或简单地说，c.e.）的字问题来实现。结构（如C. E.半群、群和环），其中实现意味着落入相同的约简度（在通常称为“可计算约简”的等价关系的约简概念下），或落入相同的同构类型（具有由可计算函数诱导的同构），或落入相同的强同构类型（具有由自然数的可计算置换诱导的同构）。例如，我们观察到每个ceer都同构于某个c.e.的字问题。但（回答了Gao和Gerdes的一个问题）并不是每一个中心都与某些非周期半群的字问题处于相同的约化度，也不是每一个中心都与某些非周期半群的约化度相同。我们还证明了Peano算术的可证等价所提供的ceer与某些非交换的非布尔运算的字问题具有相同的强同构类型。戒指
英文摘要：
This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called "computable reducibility"), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation of the natural numbers). We observe for instance that every ceer is isomorphic to the word problem of some c.e. semigroup, but (answering a question of Gao and Gerdes) not every ceer is in the same reducibility degree of the word problem of some finitely presented semigroup, nor is it in the same reducibility degree of some non-periodic semigroup. We also show that the ceer provided by provable equivalence of Peano Arithmetic is in the same strong isomorphism type as the word problem of some non-commutative and non-Boolean c.e. ring.
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。
