论文标题
结合决定论和不确定性
Combining Determinism and Indeterminism
论文作者
论文摘要
我们的目标是构建数学操作，这些数学操作结合了从量子随机性与计算确定论测量的不确定性，以便在计算中保留非机械行为。正式地，在此处证明了有关用于计算的枚举（C.E.）和双免疫集的操作的一些结果，其中目的是为了保留双权利的行动。在自然数量上开发重排操作的同时，我们发现双免疫重排产生了无限对称群体（sym $（\ mathbb {n}）$）的无数亚组，对自然数字$ \ m athbbb {n} $。 这个新的无数亚组称为双免疫对称组。我们表明，双免疫对称组包含自然数上的粉饰对称组，因此具有高度传递性。此外，相对于点的收敛拓扑，双免疫对称群在sym $（\ mathbb {n}）$中密集。一个或多个双免疫重排产生的Bi-Mumune对称组及其亚组的完整结构尚不清楚。
Our goal is to construct mathematical operations that combine indeterminism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about operations applied to computably enumerable (c.e.) and bi-immune sets are proven here, where the objective is for the operations to preserve bi-immunity. While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group (Sym$(\mathbb{N})$) on the natural numbers $\mathbb{N}$. This new uncountable subgroup is called the bi-immune symmetric group. We show that the bi-immune symmetric group contains the finitary symmetric group on the natural numbers, and consequently is highly transitive. Furthermore, the bi-immune symmetric group is dense in Sym$(\mathbb{N})$ with respect to the pointwise convergence topology. The complete structure of the bi-immune symmetric group and its subgroups generated by one or more bi-immune rearrangements is unknown.
