Title

Some Nonstandard Methods Applied to Distributive Lattices

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.

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.

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