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...

B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers on Diophantine problems. Ax was...

Kochen and Ax also co-authored the Ax–Kochen theorem, an application of model theory to algebra. In 1967 Kochen and Ernst Specker proved the Kochen–Specker...

is also true for almost all Fp((t)). An application of this is the Ax–Kochen theorem describing zeros of homogeneous polynomials in Qp. Tamely ramified...

theory) ATS theorem (number theory) Auxiliary polynomial theorem (Diophantine approximation) Ax–Kochen theorem (number theory) Baker's theorem (number theory)...

all p-adic fields are C2; see Ax–Kochen theorem or Brauer's theorem on forms. Artin had also conjectured Hasse's theorem on elliptic curves This disambiguation...

special case of Artin's conjecture on diophantine equations, the Ax–Kochen theorem. The ultraproduct construction also led to Abraham Robinson's development...

a conjecture of Jean-Louis Colliot-Thélène which generalizes the Ax–Kochen theorem. In 2002 Denef was an Invited Speaker at the International Congresses...

logic) Differentially closed field Exponential field Ax–Grothendieck theorem Ax–Kochen theorem Peano axioms Non-standard model of arithmetic First-order...

of Emil Artin, which suitably modified had just been proved as the Ax-Kochen theorem. In 1977, he proved that if p is an odd prime number, and the natural...

Historic Interest or Natural Beauty. James Ax and Simon B. Kochen make the first proof of the Ax–Kochen theorem. James Cooley and John Tukey publish the...

Brauer group and the Chevalley–Warning theorem. It stalled in the face of counterexamples; but see Ax–Kochen theorem from mathematical logic. Reduction modulo...

C2, but Guy Terjanian found p-adic counterexamples for all p. The Ax–Kochen theorem applied methods from model theory to show that Artin's conjecture...

18 variables that has no non-trivial zero. On the other hand, the Ax–Kochen theorem shows that for any fixed degree Artin's conjecture is true for all...

Nelson Cole Prize in Number Theory; proved Ax–Grothendieck theorem and Ax–Kochen theorem; Guggenheim Fellow Russell A. Kirsch ENG Developed the first...

&al (2006), chapter 2 ("Real Closed Fields"), theorem 2.91 (p. 75) Cherlin (1976), chapter 2 ("The Ax–Kochen–Ershof Transfer Principle"), §7 ("Puiseux series...

Mathematicae, 41 (2): 203–271, doi:10.4064/fm-41-2-203-271, MR 0072131. Ax, James; Kochen, Simon (1965), "Diophantine problems over local fields. II. A complete...

rationality of the zeta function of an algebraic variety" 1967 James Ax Simon B. Kochen for a series of three joint papers "Diophantine problems over local...