Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The independence of certain axioms of structures in sets


Author: Japheth Hall
Journal: Proc. Amer. Math. Soc. 31 (1972), 317-325
DOI: https://doi.org/10.1090/S0002-9939-1972-0291047-X
MathSciNet review: 0291047
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: The independence of the axioms for spans and the independence of the axioms for closure structures are usually taken for granted. In this paper, the author establishes the independence of monotonicity, extensiveness, idempotence, the exchange property, the property of having $ \emptyset $ as a fixed set and two covering properties ($ \alpha $-character, with $ \alpha $ being some cardinal number, and a covering property with respect to generators). The independence of the axioms for closure structures and spans follow immediately. It is shown that any proof of the independence of a given axiom must involve an example with certain restrictions on the cardinal number $ \alpha $.


References [Enhancements On Off] (What's this?)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291047-X
Keywords: Structures in sets, closure operations, finitary closure operations, spans
Article copyright: © Copyright 1972 American Mathematical Society