Geodesic
The quotient algebra of labeled forests modulo $h$-equivalence
Algebra i logika, Tome 46 (2007) no. 2, pp. 217-243

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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.
Keywords: labeled forest, difference hierarchy.
Mots-clés : partition 
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     author = {V. L. Selivanov},
     title = {The quotient algebra of labeled forests modulo $h$-equivalence},
     journal = {Algebra i logika},
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     volume = {46},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_2_a2/}
}
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V. L. Selivanov. The quotient algebra of labeled forests modulo $h$-equivalence. Algebra i logika, Tome 46 (2007) no. 2, pp. 217-243. http://geodesic.mathdoc.fr/item/AL_2007_46_2_a2/