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locally finite tree; one-way infinite path; acyclic monounary algebra; tree semilattice

References:

[1] R. Halin: **Über unendliche Wege in Graphen**. Math. Ann. 157 (1964), 125–137. DOI 10.1007/BF01362670 | MR 0170340 | Zbl 0125.11701

[2] L. Nebeský: **Algebraic Properties of Trees**. Acta Univ. Carol., Philologica Monographia 25, Praha, 1969. MR 0274210

[3] L. Nebeský: **A tree as a finite set with a binary operation**. Math. Bohem. 125 (2000), 455–458. MR 1802293