Arithmetic over the rings of all algebraic integers.
Bounded statements in the theory of algebraically closed fields with distinguished automophisms.
Computing the Galois group of a linear differential equation
Decidability of the rings of real algebraic and p-adic algebraic integers.
Decidable Theories of Preordered Fields.
Der Cohensche Eliminationssatz in positiver Charakteristik
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.
Elimination theory for the ring of algebraic integers.
Erblich euklidische Körper.
Errata to the paper "Remarks of the elementary theories of formal and convergent power series" Fundamenta Mathematicae 105 (1980), pp. 229-239
Existentially closed domains with radical relations.
Extensions of Büchi's problem: Questions of decidability for addition and kth powers
We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for...
Frattini Covers and Projective Groups Without the Extension Property.
Indécidabilité de la théorie des anneaux de séries formelles à plusieurs indéterminées
Nice local global fields. IV.
Non-axiomatizable classes of V-topological fields.
Properties of extensions of algebraically maximal fields.
We prove some properties similar to the theorem Ax-Kochen-Ershov, in some cases of pairs of algebraically maximal fields of residue characteristic p > 0. This properties hold in particular for pairs of Kaplansky fields of equal characteristic, formally p-adic fields and finitely ramified fields. From that we derive results about decidability of such extensions.
Rekursive Unentscheidbarkeit der Theorie der pythagoräischen Körper
Remarks on the elementary theories of formal and convergent power series