Existence of rational points on smooth projective varieties
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...
Functorial concepts of complexity for finite automata.
Geometrical model theory.
Goldbach conjecture.
H. L. M. (Hrushovski-Lang-Mordell)
Hilbert's Tenth Problem for fields of rational functions over finite fields.
Kneser’s theorem for upper Banach density
Suppose is a set of non-negative integers with upper Banach density (see definition below) and the upper Banach density of is less than . We characterize the structure of by showing the following: There is a positive integer and a set , which is the union of arithmetic sequences [We call a set of the form an arithmetic sequence of difference and call a set of the form an arithmetic progression of difference . So an arithmetic progression is finite and an arithmetic sequence...
Models of arithmetic and the 1-3-1 lattice
Nicht-Standardmodelle der Zahlentheorie.
Nonstandard arithmetic of iterated polynomials.
O desátém Hilbertově problému
On expansions of β-models
On some problems in
On the Goldbach conjecture and the consistency of general recursive arithemetic.
On the ranges of discrete exponentials.
Ordered ultraconnected rings
Proof of the quadratic reciprocity law in primitive recursive arithmetic.
Real classes in the ultrapower of hereditarily finite sets
Reduction of an arbitrary diophantine equation to one in 13 unknowns