Decidability of the rings of real algebraic and p-adic algebraic integers.
Decidable Theories of Preordered Fields.
Definable sets over finite fields.
Definable subgroups of algebraic groups over finite fields.
Der Cohensche Eliminationssatz in positiver Charakteristik
Der Hilbertsche Irreduzibilitätssatz.
Diophantine representation of Mersenne and Fermat primes
Diophantine undecidability for addition and divisibility in polynomial rings
We prove that the positive-existential theory of addition and divisibility in a ring of polynomials in two variables A[t₁,t₂] over an integral domain A is undecidable and that the universal-existential theory of A[t₁] is undecidable.