Metadata about: In this paper we consider two classes of posets labeled over an alphabet A. The class [Formula: see text] is built from the letters and closed under the operations of series finite, [Formula: see text] and [Formula: see text] products, and finite parallel product. In the class [Formula: see text], [Formula: see text] and [Formula: see text] products are replaced by [Formula: see text] and [Formula: see text] powers. We prove that [Formula: see text] and [Formula: see text] are freely generated in their respective natural varieties of algebras [Formula: see text] and [Formula: see text], and that the equational theory of [Formula: see text] is decidable.

About: In this paper we consider two classes of posets labeled over an alphabet A. The class [Formula: see text] is built from the letters and closed under the operations of series finite, [Formula: see text] and [Formula: see text] products, and finite parallel product. In the class [Formula: see text], [Formula: see text] and [Formula: see text] products are replaced by [Formula: see text] and [Formula: see text] powers. We prove that [Formula: see text] and [Formula: see text] are freely generated in their respective natural varieties of algebras [Formula: see text] and [Formula: see text], and that the equational theory of [Formula: see text] is decidable.

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