标题： 可能同构的结构 显示英文标题

标题： Probably isomorphic structures

摘要： 两个在同一种语言中的结构$M, N$被称为可能同构，如果它们（或者在度量结构的情况下，它们的完成）在用勒贝格测度代数进行强制后是同构的。 我们证明，如果$M$和$N$是离散结构，或者非退化单纯理论的极值模型，那么$M$和$N$可能同构当且仅当$L^1([0,1], M) \cong L^1([0,1], N)$。 我们还利用用于证明上述结果的一些集合论论证来刻画非平凡超乘积的扩散冯·诺依曼代数何时是张量素的。 显示英文摘要

摘要： Two structures $M, N$ in the same language are called probably isomorphic if they (or, in case of metric structures, their completions) are isomorphic after forcing with the Lebesgue measure algebra. We show that, if $M$ and $N$ are discrete structures, or extremal models of a non-degenerate simplicial theory, then $M$ and $N$ are probably isomorphic if and only if $L^1([0,1], M) \cong L^1([0,1], N)$. We moreover employ some of the set-theoretic arguments used to prove the aforementioned result to characterize when nontrivial ultraproducts of diffuse von Neumann algebras are tensorially prime.