The typical countable algebra

Details The typical countable algebra The typical countable algebra

2008-01-08

arxiv.org/abs/0801.1212v1

Mathematics

Rings and Algebras

Scientific paper

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.

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