On models of exponentiation. Identities in the HSI-algebra of posets

Mathematical Logic Quarterly 54 (3):280-287 (2008)
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Abstract

We prove that Wilkie's identity holds in those natural HSI-algebras where each element has finite decomposition into components.Further, we construct a bunch of HSI-algebras that satisfy all the identities of the set of positive integers ℕ. Then, based on the constructed algebras, we prove that the identities of ℕ hold in the HSI-algebra of finite posets when the value of each variable is a poset having an isolated point

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