The quotient algebra of labeled forests modulo h-equivalence

We introduce and study some natural operations on a structure of finite labeled forests, which is crucial in extending the difference hierarchy to the case of partitions. It is shown that the corresponding quotient algebra modulo the so-called h-equivalence is the simplest non-trivial semilattice with discrete closures. The algebra is also characterized as a free algebra in some quasivariety. Part of the results is generalized to countable labeled forests with finite chains. Supported by a DAAD project within the program “Ostpartnerschaften.” __________ Translated from Algebra I Logika, Vol. 46, No. 2, pp. 217–243, March–April, 2007.