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On many-sorted algebraic closure operators

✍ Scribed by Juan Climent Vidal; Juan Soliveres Tur

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 96 KB
Volume: 266
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310146

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✦ Synopsis

Abstract

A theorem of Birkhoff‐Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many‐sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many‐sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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