论文标题
模块化量子逻辑中的重言术测试集
Test sets for tautologies in modular quantum logic
论文作者
论文摘要
正如Dunn，Moss和Wang所定义的那样，Ortholattice $ L $中的通用测试集是一个子集$ t $，因此每个学期在$ t $ from $ t $的所有替换下都具有值为$ 1 $的值。将其概括为有限维式希尔伯特空间子空间的矫形器的结果，我们表明，没有有限尺寸的无限模块化矫形器可以接受有限的通用测试集。另一方面，回答了同一作者的问题，我们为任何类型II型$ _1 $ _1 $ _1 $ von Neumann代数因素以及冯·诺伊曼（Von Neumann）的代数结构的矫形器提供了可数的通用测试集。这些通用测试集包括具有合理归一化尺寸的元素，分母的功率为$ 2 $。
As defined by Dunn, Moss, and Wang, an universal test set in an ortholattice $L$ is a subset $T$ such that each term takes value $1$, only, if it does so under all substitutions from $T$. Generalizing their result for ortholattices of subspaces of finite dimensional Hilbert spaces, we show that no infinite modular ortholattice of finite dimension admits a finite universal test set. On the other hand, answering a question of the same authors, we provide a countable universal test set for the ortholattice of projections of any type II$_1$ von Neumann algebra factor as well as for von Neumann's algebraic construction of a continuous geometry. These universal test sets consist of elements having rational normalized dimension with denominator a power of $2$.
