Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-04T09:17:51.243Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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