Mutually algebraic structures and expansions by predicates
Mutually algebraic structures and expansions by predicates
复制标题
互代数结构和谓词展开
DOI：
10.2178/jsl.7801120
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. Laskowski
中科院分区：
文献类型：
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作者：
M. Laskowski
摘要引入了相互代数结构和理论的概念，并证明了它们的许多等价性。理论T互代数当且仅当它是弱极小平凡的当且仅当没有T的模型M有一个具有有限覆盖性质的一元谓词的展开(M，A)。我们证明了每个结构都有最大互代数约简。并给出了固定互代数结构的初等扩张类的一个强结构定理。
Abstract We introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model M of T has an expansion (M, A) by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct. and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic structure.