We investigate several consequences of inclusion relations between quantified provability logics. Moreover, we give a necessary and sufficient condition for the inclusion relation between quantified provability logics with respect to \(\Sigma _1\) arithmetical interpretations.

中文翻译：

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关于量化可证明性逻辑之间的包含

我们研究了量化可证明性逻辑之间包含关系的几个后果。此外，我们针对\(\Sigma _1\)算术解释给出了量化可证明性逻辑之间包含关系的充要条件。