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Let p be a prime number, K a number field, and S a finite set of places of K. Let KS be the compositum of all extensions of K (in a fixed algebraic closure K) which are unramified outside S, and put GK,S = Gal(KS/K) for its Galois group. These arithmetic fundamental groups play a very important role in number theory. Algebraic geometry provides the most… (More)

- Wayne Aitken, Donald J. Niederpruem
- Journal of bacteriology
- 1970

Electron microscopic features and biochemical events were outlined in basidiospore germination of Schizophyllum commune. Normal ultrastructural changes included prominent vacuolization and more abundant endoplasmic reticulum. A lag phase in outgrowth included depletion of cellular reserves of trehalose, mannitol, and arabitol and subsequent increases in… (More)

- Wayne Aitken
- J. Comb. Theory, Ser. A
- 1999

- Wayne Aitken, Jeffrey A. Barrett
- J. Philosophical Logic
- 2004

- Wayne Aitken, Jeffrey A. Barrett
- J. Philosophical Logic
- 2007

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)

- Wayne Aitken, Jeffrey A. Barrett
- J. Philosophical Logic
- 2008

- Wayne Aitken, Franz Lemmermeyer
- The American Mathematical Monthly
- 2011

This article explains the Hasse principle and gives a self-contained development of certain counterexamples to this principle. The counterexamples considered are similar to the earliest counterexample discovered by Lind and Reichardt. This type of counterexample is important in the theory of elliptic curves: today they are interpreted as nontrivial elements… (More)

After Hasse had found the first example of a Local-Global principle in the 1920s by showing that a quadratic form in n variables represented 0 in rational numbers if and only if it did so in every completion of the rationals, mathematicians investigated whether this principle held in other situations. Among the first counterexamples to the Hasse principle… (More)

We call a pair of polynomials f, g ∈ Fq[T ] a Davenport pair (DP) if their value sets are equal, Vf(Fqt) = Vg(Fqt), for infinitely many extensions of Fq. If they are equal for all extensions of Fq (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. Monodromy/Galois-theoretic… (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)