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On models of exponentiation. Identities in the HSI‐algebra of posets
Author(s) -
Asatryan Gurgen
Publication year - 2008
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710031
Subject(s) - exponentiation , mathematics , partially ordered set , star product , identity (music) , element (criminal law) , set (abstract data type) , pure mathematics , construct (python library) , algebra over a field , combinatorics , discrete mathematics , computer science , mathematical analysis , physics , political science , acoustics , law , programming language
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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)