The lattice of convexities of partial monounary algebras (Q1646610)

Extending the work of the second author [Algebra Univers. 60, No. 2, 125--143 (2009; Zbl 1185.08001)] to a slightly more general notion of convexity, the authors prove an intricate decomposition theorem for the lattice \(K\) of all convexities of partial monounary algebras under inclusion. In \(K\), each convexity can be generated by at most two of its members, the convexity of all partial monounary algebras being generated by the integers endowed with the successor operation. It comes as no surprise that \(K\) is countably infinite.