Some Finiteness Conditions in Lattices Using Nonstandard Proof Methods

Author

Matt Insall, Missouri University of Science and TechnologyFollow

Abstract

One of the early themes in nonstandard analysis is a characterization of hereditary finite properties of algebraic structures in terms of their hyperfinite extensions. The results of this type, practically always obtained as a simple consequence of upward and downward transfer principles, are used here in the category of lattices for analyzing properties such as existence of (local) polarities. A typical result (Proposition 2.1) says that a pair of functions f, g:L ! L is a local polarity of L if and only if L has a hyperfinitely generated extension L_ for which (_f|L_, _g|L_) is a (hyper)polarity of L_. Among other properties of lattices analyzed from this point of view are tightness, 0, 1-simplicity, etc.

Recommended Citation

M. Insall, "Some Finiteness Conditions in Lattices Using Nonstandard Proof Methods," Journal of the Australian Mathematical Society, American Mathematical Society, Jan 1992.

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

1446-7887

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1992 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 1992