 Ax–Kochen theorem

The Ax–Kochen theorem, named for James Ax and Simon B. Kochen, states that for each positive integer "d" there is a finite set "Yd" of prime numbers, such that if "p" is any prime not in "Yd" then every homogeneous polynomial of degree "d" over the p-adic numbers in at least "d"2 + 1 variables has a nontrivial zero.The proof of the theorem makes extensive use of methods from mathematical logic, such as model theory.