Abstract:
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.
Citation:
V. L. Selivanov, “The quotient algebra of labeled forests modulo $h$-equivalence”, Algebra Logika, 46:2 (2007), 217–243; Algebra and Logic, 46:2 (2007), 120–133