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Content available remote Subdirect product representations of some unary extensions of semilattices
EN
An algebra [...] represents the sequence so = (0, 3, l, l, . . .) if there are no constants in [...], there are exactly 3 distinct essentially unary polynomials in [...] and exactly l essentially n-ary polynomial in [...] for every n > l . It was proved in [4] that an algebra [..] represents the sequence so if and only if it is clone equivalent to a generic of one of three varieties V1, V2, V3, see Section l of [4]. Moreover, some representations of algebras from these varieties by means of semilattice ordered systems of algebras were given in [4] . In this paper we give another, by subdirect products, representation of algebras from V1, V2, V3. Moreover, we describe all subdirectly irreducible algebras from these varieties and we show that if an algebra [...] represents the sequence so, then it must be of cardinality at least 4.
2
Content available remote Characterizations of posets via weak states
EN
Weak states on posets are defined which are in some analogy to states on orthomodular posets used in axiomatic quantum mechanics. It is shown how certain properties of the set of weak states characterize certain properties of the underlying poset.
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