当前位置: X-MOL 学术Sib. Adv. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Definable Sets in Generic Structures and their Cardinalities
Siberian Advances in Mathematics Pub Date : 2018-03-08 , DOI: 10.3103/s1055134418010030
Y. Kiouvrekis , P. Stefaneas , S. V. Sudoplatov

Analyzing diagrams forming generative classes, we describe definable sets and their links in generic structures as well as cardinality bounds for these definable sets, finite or infinite. Introducing basic characteristics for definable sets in generic structures, we compare them each others and with cardinalities of these sets.We introduce calculi for (type-)definable sets allowing to compare their cardinalities. In terms of these calculi, Trichotomy Theorem for possibilities comparing cardinalities of definable sets is proved. Using these calculi, we characterize the possibility to construct a generic structure of a given generative class.

中文翻译:

通用结构及其基数的可定义集合

分析构成生成类的图,我们在通用结构中描述了可定义集及其链接,以及这些可定义集(有限或无限)的基数范围。在介绍通用结构中可定义集合的基本特征后,我们将它们相互比较并与这些集合的基数进行比较。我们为(类型)可定义集合引入计算以比较其基数。根据这些结石,证明了三分定理用于比较可定义集合的基数的可能性。使用这些计算,我们表征了构造给定生成类的通用结构的可能性。
更新日期:2018-03-08
down
wechat
bug