Some Nonstandard Methods Applied to Distributive Lattices

Author

Mai Gehrke
Matt Insall, Missouri University of Science and TechnologyFollow
Klaus Kaiser

Abstract

Every distributive lattice D can be seen as a sublattice of a hyperfinite lattice. This simple and useful observation, which holds for all locally finite algebras, permits the authors to give proofs of some well-known fundamental theorems about distributive lattices on the basis of the transfer principle. They use the hyperfinite extensions to characterize standard properties of lattices; e.g., they show (Proposition 4) that a distributive lattice is injective if and only if it is a retract of all of its hyperfinite extensions.

Recommended Citation

M. Gehrke et al., "Some Nonstandard Methods Applied to Distributive Lattices," Z. Math. Logik Grundlag. Math, American Mathematical Society, Jan 1990.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Distributive lattice; Nonstandard

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1990 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 1990