We consider algebras of binary formulas for compositions of theories both in the general case and as applied to ℵ0-categorical, strongly minimal, and stable theories, linear preorders, cyclic preorders, and series of finite structures. It is shown that edefinable compositions preserve isomorphisms and elementary equivalence and have basicity formed by basic formulas of the initial theories. We find criteria for e-definable compositions to preserve ℵ0-categoricity, strong minimality, and stability. It is stated that e-definable compositions of theories specify compositions of algebras of binary formulas. A description of forms of these algebras is given relative to compositions with linear orders, cyclic orders, and series of finite structures.

中文翻译：

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理论组合的二元公式代数

我们考虑在一般情况下和应用于 ℵ0 分类、强极小和稳定理论、线性预序、循环预序和有限结构系列的二元公式的代数。结果表明，可定义组合保留了同构性和基本等价性，并具有由初始理论的基本公式形成的基本性。我们找到了电子可定义组合的标准，以保持 ℵ0 类别、强最小性和稳定性。据说e-可定义理论组合指定了二元公式代数的组合。这些代数的形式的描述是相对于具有线性阶次、循环阶次和有限结构系列的组合给出的。