什么时候初等双嵌入性意味着同构？
When does elementary bi-embeddability imply isomorphism?
摘要：
一个一阶理论具有Schroder-Bernstein性质，如果它的任意两个基本双嵌入的模型是同构的。我们证明了如果一个可数理论T具有Schroder-Bernstein性质，那么它是可分类的（它是超稳定的，并且具有NDOP和NOTOP），并且满足一个比非多维性稍强的条件，即：不存在T的模型M，M上的类型p，以及M的自同构f使得对于每两个不同的自然数i和j，f^i（p）与f^j（p）正交。我们还对如何刻画具有Schroder-Bernstein性质的理论类作了一些说明。
英文摘要：
A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if a countable theory T has the Schroder-Bernstein property then it is classifiable (it is superstable and has NDOP and NOTOP) and satisfies a slightly stronger condition than nonmultidimensionality, namely: there cannot be a model M of T, a type p over M, and an automorphism f of M such that for every two distinct natural numbers i and j, f^i(p) is orthogonal to f^j(p). We also make some conjectures about how the class of theories with the Schroder-Bernstein property can be characterized.
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。
