论文标题
随机对的近似同构
Approximate isomorphism of randomization pairs
论文作者
论文摘要
从连续逻辑的意义上讲，我们研究了近似$ \ aleph_0 $ - 随机化的理论的分类。 这导致我们通过展示$ \ aleph_0 $ -scaterical，$ \ aleph_0 $ - 稳定的度量理论$ q $，对相应理论$ q_p $ q_p $ q airs y y y aleph_0 $ -spatecor，i.e evecorial complatial note cymors，i.ee.e.e.e.e.e evaligor，这使我们通过展示$ \ aleph_0 $ -scategorical $ \ aleph_0 $ -spatecor，i.e.e.e.e.e.e.e.e evaligober，这使我们通过展示$ \ aleph_0 $ stable公制$ q $，甚至不是分开的模型。较小模型的扰动。这样的例子就是一个有限场上的随机无限矢量空间的理论$ q $。 从积极的一面来看，我们表明，美丽的随机无限套装的理论大约为$ \ aleph_0 $ - 分类。我们还证明，在这种情况下，相关的更强的财产在各种自然结构下是稳定的，并为普通案例制定了我们的猜测。
We study approximate $\aleph_0$-categoricity of theories of beautiful pairs of randomizations, in the sense of continuous logic. This leads us to disprove a conjecture of Ben Yaacov, Berenstein and Henson, by exhibiting $\aleph_0$-categorical, $\aleph_0$-stable metric theories $Q$ for which the corresponding theory $Q_P$ of beautiful pairs is not approximately $\aleph_0$-categorical, i.e., has separable models that are not isomorphic even up to small perturbations of the smaller model of the pair. The theory $Q$ of randomized infinite vector spaces over a finite field is such an example. On the positive side, we show that the theory of beautiful pairs of randomized infinite sets is approximately $\aleph_0$-categorical. We also prove that a related stronger property, which holds in that case, is stable under various natural constructions, and formulate our guesswork for the general case.
