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An ordered sheaf representation of subresiduated lattices

Published online by Cambridge University Press:  17 April 2009

William H. Cornish
William H. Cornish
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park 5042, South Australia, Australia.
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Abstract

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Kennison's concept of an ordered sheaf is used to show that any member of the variety of subresiduated lattices is canonically isomorphic to the algebra of all ordered sections in a certain ordered sheaf, whose base is the Priestley space of the residuating sublattice.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 1 , August 1980 , pp. 125 - 132
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Cignoli, Roberto, “The lattice of global sections of sheaves of chains over Boolean spaces”, Algebra Universalis 8 (1978), 357–373.CrossRefGoogle Scholar
[2]Cornish, William H., “On H. Priestley's dual of the category of bounded distributive lattices”, Mat. Vesnik 12 (27) (1975), 329–332.Google Scholar
[3]Davey, Brian A., “Sheaf spaces and sheaves of universal algebras”, Math. Z. 134 (1975), 275–290.CrossRefGoogle Scholar
[4]Epstein, George and Horn, Alfred, “Logics which are characterized by subresiduated lattices”, Z. Math. Logik Grundlag. Math. 22 (1976), 199–210.CrossRefGoogle Scholar
[5]Kennison, John F., “Integral domain type representations in sheaves and other topoi”, Math. Z. 151 (1976), 35–56.Google Scholar
[6]Rasiowa, Helena and Sikorski, Roman, The mathematics of metamathenatics, Second edition revised (Monografie Matematyczne 41. PWN, Warszawa, 1968).Google Scholar