Let 
be the set of primes, and
let 
and 
be the fields of p-adic
numbers and formal power series over 
. Further, suppose that 
is a "nonprincipal maximal filter" on 
. Then 
and 
are isomorphic.
Ax-Kochen Isomorphism Theorem
See also
Hyperreal Number, Nonstandard AnalysisExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Ax-Kochen Isomorphism Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ax-KochenIsomorphismTheorem.html