every ordered field with the least upper bound property is isomorphic to the real numbers

Let $F$ be an ordered field. If $F$ satisfies the least upper bound property then $F$ is isomorphic as an ordered field to the real numbers $\mathbb{R}$ .

Title	every ordered field with the least upper bound property is isomorphic to the real numbers
Canonical name	EveryOrderedFieldWithTheLeastUpperBoundPropertyIsIsomorphicToTheRealNumbers
Date of creation	2013-03-22 14:10:33
Last modified on	2013-03-22 14:10:33
Owner	archibal (4430)
Last modified by	archibal (4430)
Numerical id	4
Author	archibal (4430)
Entry type	Theorem
Classification	msc 12D99
Classification	msc 26-00
Classification	msc 54C30