  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 all the currently known classes of the
former category and establish that grids of unbounded size can indeed be
interpreted in them.
