Regarding strictly monadic second‐order logic (SMSOL), which is the fragment of monadic second‐order logic in which all predicate constants are unary and there are no function symbols, we show that a standard deductive system with full comprehension is sound and complete with respect to standard semantics. This result is achieved by showing that in the case of SMSOL, the truth value of any formula in a faithful identity‐standard Henkin structure is preserved when the structure is “standardized”; that is, the predicate domain is expanded into the set of all unary relations. In addition, we obtain a simpler proof of the decidability of SMSOL.

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关于严格一元二阶逻辑的完备性

关于严格的单子二阶逻辑（SMSOL），这是单子二阶逻辑的片段，其中所有谓词常数均为一元且没有功能符号，我们证明具有完全理解力的标准演绎系统是合理且完整的尊重标准语义。通过显示在SMSOL的情况下，当“标准化”结构时，将保留忠实的身份-标准Henkin结构中任何公式的真值，从而获得此结果；也就是说，谓词域被扩展为所有一元关系的集合。此外，我们获得了SMSOL可判定性的更简单证明。