The typical countable algebra
Rings and Algebras
2008-01-09 v1 Logic
Abstract
We argue that it makes sense to talk about ``typical'' properties of lattices, and then show that there is, up to isomorphism, a unique countable lattice L* (the Fraisse limit of the class of finite lattices) that has all ``typical'' properties. Among these properties are: L* is simple and locally finite, every order preserving function can be interpolated by a lattice polynomial, and every finite lattice or countable locally finite lattice embeds into L*. The same arguments apply to other classes of algebras assuming they have a Fraisse limit and satisfy the finite embeddability property.
Cite
@article{arxiv.0801.1212,
title = {The typical countable algebra},
author = {Martin Goldstern},
journal= {arXiv preprint arXiv:0801.1212},
year = {2008}
}