Separating Classes of Groups by First-Order Sentences
Separating Classes of Groups by First-Order Sentences
复制标题
通过一阶句子分隔组的类别
DOI：
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发表时间：
2003
影响因子：
0.8
通讯作者：
A. Nies
中科院分区：
文献类型：
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作者：
A. Nies
对于群${mathcal C}子集{mathcal D}$的类的各种真包含，我们得到一个群$Hin{mathcal D}$和一个一阶句子φ使得H ∈ φ但没有G∈ C满足φ.我们考虑的类包括有限的，提出的，生成的有和没有可解的字的问题，和所有可数群。对于一个分离，我们给出一个f.g.的例子。群，即对于某个素数p，它是唯一的f.g.满足一个适当的第一顺序句子的组。此类群的另一个例子，秩为2的自由阶-2幂零群，用于表明真正的算术Th（，+，×）可以在有限表示群类和其他fg类的理论中解释。组
For various proper inclusions of classes of groups ${mathcal C}subset{mathcal D}$, we obtain a group $Hin{mathcal D}$ and a first-order sentence φ such that H⊨φ but no G∈ C satisfies φ. The classes we consider include the finite, finitely presented, finitely generated with and without solvable word problem, and all countable groups. For one separation, we give an example of a f.g. group, namely ℤp ≀ ℤ for some prime p, which is the only f.g. group satisfying an appropriate first-order sentence. A further example of such a group, the free step-2 nilpotent group of rank 2, is used to show that true arithmetic Th(ℕ,+,×) can be interpreted in the theory of the class of finitely presented groups and other classes of f.g. groups.