On the completeness and the decidability of strictly monadic second-order logic

被引：0
|
作者：
Takagi, Kento [1 ]
Kashima, Ryo [1 ]
机构：
[1] Tokyo Inst Technol, Dept Math & Comp Sci, Meguro Ku, 2-12-1 Ookayama, Tokyo 1528552, Japan
来源：
MATHEMATICAL LOGIC QUARTERLY | 2020年 / 66卷 / 04期
关键词：
D O I：
10.1002/malq.201900046
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (c) 2021 Wiley-VCH GmbH
引用
收藏
页码：438 / 447
页数：10
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