| Abstract:
There are two standard constructions of the lattice ordered ring of real
numbers R from the lattice ordered ring of rational numbers
Q. The first, due to Dedekind, constructs the poset R from
the poset Q and extends the operations from Q to R.
The second, due to Cauchy constructs R as a quotient of a
subalgebra of a countable power of Q (that is, as the quotient of
the lattice ordered ring of countable rational Cauchy sequences by the
convex ideal of zero- convergent countable rational sequences). There is a
third path, due to Abraham Robinson, which constructs R as a
quotient of a subalgebra of an ultrapower of Q. I will review the
first two constructions and go into detail about the third.
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