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Kernels of epimorphisms of finitely generated free lattices

Original research by William DeMeo, Peter Myer, and Nik Ruskuc.

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The notes in the directory tex-notes give a proof of the following:

Theorem. Let $X$ be a finite set and $\mathbf F := \mathbf F(X)$ the free lattice generated by $X$. Suppose $\mathbf L = \langle L, \wedge, \vee\rangle$ is a finite lattice and $h\colon \mathbf{F} \rightarrow \mathbf{L}$ a lattice epimorphism. Then $h$ is bounded iff the kernel of $h$ is a finitely generated sublattice of $\mathbf F \times \mathbf F$.