# 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 EveryOrderedFieldWithTheLeastUpperBoundPropertyIsIsomorphicToTheRealNumbers 2013-03-22 14:10:33 2013-03-22 14:10:33 archibal (4430) archibal (4430) 4 archibal (4430) Theorem msc 12D99 msc 26-00 msc 54C30