Some Nonstandard Methods Applied to Distributive Lattices
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.
M. Gehrke et al., "Some Nonstandard Methods Applied to Distributive Lattices," Z. Math. Logik Grundlag. Math, American Mathematical Society, Jan 1990.
Mathematics and Statistics
Keywords and Phrases
Distributive lattice; Nonstandard
Article - Journal
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