| Abstract:
The urexample of a lattice-ordered group or ring is the reals R under the
usual (linear) ordering. The examples mushroom from here. Two examples:
- Every lattice-ordered group can be embedded into the
lattice-ordered
group of all order isomorphisms of some chain (linearly ordered set).
- If c is the power of the continuum, then there
2c non-isomorphic
ways to order R to produce a lattice-ordered ring; moreover, in each of
them Q is linearly ordered as usual.
In this first lecture, I will discuss their arithmetic and construct some
interesting examples.
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