If M and Nare ordered groups, we denote by Mx N the group MxNequipped with the lexicographical order: (a,b) < (a',b') if and only if a < a' or {a = a' and b < b'). In [1], A. L. S. Corner gives an example of two countable abelian groups A, G such that G and A x A x G are isomorphic while G and A x G are not isomorphic; he also gives an example of two nonisomorphic countable abelian groups G, H ...

Let K and L be ordered algebraic extensions of an ordered field F. Suppose K and L are Henselian with Archimedean real closed residue class fields. Then K and L are shown to be F-isomorphic as ordered fields if they have the same value group. Analogues to this result are proved involving orderings of higher level, unordered extensions, and, when K and L are maximal valued fields, transcendental...