A solution to identities problem in 2‐element HSI‐algebras

Asatryan, Gurgen

doi:10.1002/malq.200310087

Mathematical Logic Qtrly

2004

DOI: 10.1002/malq.200310087

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A solution to identities problem in 2‐element HSI‐algebras

Gurgen Asatryan

Abstract: All arithmetical identities involving 1, addition, multiplication and exponentiation are valid in every 2‐element HSI‐algebra. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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

Asatryan¹

2008

Mathematical Logic Qtrly

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

Asatryan¹

2008

Mathematical Logic Qtrly

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The saga of the High School Identities

Burris

Yeats

2005

Algebra univers.

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A solution to identities problem in 2‐element HSI‐algebras

Abstract: All arithmetical identities involving 1, addition, multiplication and exponentiation are valid in every 2‐element HSI‐algebra. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cited by 2 publications

References 7 publications

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

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

The saga of the High School Identities

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