Seese's conjecture for finite graphs states that monadic second-order logic (MSO) is undecidable on all graph classes of unbounded clique-width. We show that to establish this it would suffice to show that grids of unbounded size can be interpreted in two families of graph classes: minimal hereditary classes of unbounded clique-width; and antichains of unbounded clique-width under the induced subgraph relation. We explore a number of known examples of the former category and establish that grids of unbounded size can indeed be interpreted in them.

中文翻译：

---

一些无界集团宽度的遗传类的 MSO 不可判定性

Seese 对有限图的猜想指出，一元二阶逻辑 (MSO) 在所有无界集团宽度的图类上都是不可判定的。我们表明，要建立这一点，只要证明无界大小的网格可以解释为两个图类家族就足够了：无界集团宽度的最小遗传类；和在诱导子图关系下无界集团宽度的反链。我们探索了前一类的许多已知示例，并确定确实可以在其中解释无限大小的网格。