Learn More
Let K be a number field, t a parameter, F = K(t), and ϕ(x) ∈ K[x] a polynomial of degree d ≥ 2. The polynomial Φ n (x, t) = ϕ • n (x)−t ∈ F [x], where ϕ • n = ϕ • ϕ • · · · • ϕ is the n-fold iterate of ϕ, is absolutely irreducible over F ; we compute a recursion for its discriminant. Let F ϕ be the field obtained by adjoining to F all roots (in a fixed F)(More)
We call a pair of polynomials f, g ∈ F q [T ] a Davenport pair (DP) if their value sets are equal, V f (F q t) = V g (F q t), for infinitely many extensions of F q. If they are equal for all extensions of F q (for all t ≥ 1), then we say (f, g) is a strong Davenport pair (SDP). Exceptional polynomials and SDP's are special cases of DP's.(More)
Algorithmic logic is the logic of basic statements concerning algorithms and the algorithmic rules of deduction between such statements. It is a type-free logic capable of significant self-reference. Because of its expressive strength, traditional rules of logic are not necessarily valid. As shown in [1], the threat of paradoxes, such as the Curry paradox ,(More)
α-recursion lifts classical recursion theory from the first transfinite ordinal ω to an arbitrary admissible ordinal α [13]. Turing machine models for α-recursion and other types of transfinite computation have been proposed and studied [5] and [7] and are applicable in computational approaches to the foundations of logic and mathematics [11]. They also(More)
  • 1