We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is independent on the choice of a particular successor. We show that when the degree is bounded, successor-invariant first-order logic is no more expressive than first-order logic.

中文翻译：

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有界度类的后继不变一阶逻辑

我们研究后继不变一阶逻辑的表达能力，这是一阶逻辑的扩展，允许在结构上使用额外的后继关系，只要公式的有效性独立于选择特定的继任者。我们表明，当度数有界时，后继不变的一阶逻辑并不比一阶逻辑更具表现力。