There is an error in the proof of the main theorem on page 6 (''Rice's Theorem for Logic''). If φ is undecidable in Q, the claim that Ax1 and Ax2 are tautologies is not valid, and this fact compromises the rest of the proof. Furthermore, the following decidable property is a counterexample to our result: Definition 1. Let T be a theory. A theory T + is an extension of T if Th(T) ⊆ Th(T +). Defi...

Let E be a group extension of an abelian l.c.s.c. group A by an amenable l.c.s.c. group G. We say that an ergodic action V of A is extendible to an action W of E if V (A) is isomorphic to W (A). It turns out that the extendibility property can be described in terms of cocycles over a skew product taking values in A. For topologically trivial group extensions E(G,A), we prove that the extendibil...

I now want to apply the basic notions of computational representations and abstract algebra that I have developed so far to concrete algorithms, and briefly to consider their complexity. As I explained earlier, underlying all of computer algebra are the integers, so I will begin by considering algorithms for performing arithmetic on integers of unlimited magnitude, which I will call long intege...

We give a criterion for an HNN extension of a finite p-group to be residually p. 1. Statement of the Main Results By an HNN pair we mean a pair (G,φ) where G is a group and φ : A → B is an isomorphism between subgroups A and B of G. Given such an HNN pair (G,φ) we consider the corresponding HNN extension G∗ = 〈G, t | t−1at = φ(a), a ∈ A〉 of G, which we denote, by slight abuse of notation, as G∗...

Abstract. This paper presents an extension of the Generative Dependency Grammar (GDG) and GDG with Feature Structure (FS). The extension consist of the indirect dependency notion introduction. The direct dependencies allows to expres some relations between elements (for exemples non-terminals) belonging to the the right side of a single grammar rule. The indirect relations will allow to express...

A Chern-Simons action for supergravity in odddimensional spacetimes is proposed. For all odd dimensions, the local symmetry group is a non trivial supersymmetric extension of the Poincaré group. In 2 + 1 dimensions the gauge group reduces to super-Poincaré, while for D = 5 it is superPoincaré with a central charge. In general, the extension is obtained by the addition of a 1-form field which tr...

For a real abelian number field F and for a prime p we study the relation between the p-parts of the class groups and of the quotients of global units modulo cyclotomic units along the cyclotomic Zp-extension of F . Assuming Greenberg’s conjecture about the vanishing of the λ-invariant of the extension, a map between these groups has been constructed by several authors, and shown to be an isomo...