This work is a development of some model-theoretic aspects of the theory of Special Groups ([9]) − a first order axiomatization of the algebraic theory of quadratic forms. In [33] we constructed a functor, the profinite hull functor, P, from the category RSG of reduced special groups with SG-morphisms to the category RSGpf of profinite reduced special groups with continuous SG-morphisms. From r...

Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p > 0 of countable cardinality. Let N be a normal (resp. characteristic) subgroup of π1(C). Under the hypothesis that the quotient π1(C)/N admits an infinitely generated Sylow p-subgroup, we prove that N is indeed isomorphic to a normal (resp. characteris...

We construct and study the moduli of continuous representations of a profinite group with integral p-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is algebraizable. When this profinite group is the absolute Galois group of a p-adic local field, we show that these moduli spaces admit Zariski-closed loci cutti...

THEOREM. Let F be the free profinite group on a set X, where \X\ > 2, and let n be a non-empty set of primes. Then F has a maximal abelian subgroup isomorphic to HpEn Zp. The idea of the proof is the following: we show that A — Ylpe7I1p is a free factor of Pa, i.e. fia ^ A *B for some profinite group B. To conclude from this that A is a maximal abelian subgroup of Fa (the general case then foll...

We extend a finite group solvability criterion of J.G. Thompson, based on his classification of finite minimal simple groups, to a prosolvability criterion. Moreover, we generalize to the profinite setting subsequent developments of Thompson’s criterion by G. Kaplan and the second author, which recast it in terms of properties of sequences of Sylow subgroups and their products. This generalizat...

In this paper we consider a general way of constructing profinite structures based on a given framework — a countable family of objects and a countable family of recognisers (e.g. formulas). The main theorem states: A subset of a family of recognisable sets is a lattice if and only if it is definable by a family of profinite equations. This result extends Theorem 5.2 from [GGEP08] expressed onl...

Let R be a real closed field and L be a finite extension of R(t). We prove that Gal(L) ∼= Gal(R(t)) if L is formally real and Gal(L) is the free profinite group of rank card(R) if L is not formally real. MR Classification: 12E30 Directory: \Jarden\Diary\RealFree 3 April, 2007 * Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation....

A practicable approach to diagram completion is to first compute model completions on the abstract syntax level. These can be translated to corresponding diagram changes by the layout engine afterwards. Normally, several different model completions are possible though. One way to deal with this issue is to let the user choose among them explicitly, which is already helpful. However, such a choi...

The terms that users pass to search engines are often ambiguous, by referring to homonyms. The search results in these cases are a mixture of links to documents that refer to different meanings of the search terms. Current search engines provide suggested query completion terms as a dropdown list. However, such lists are not well organized, mixing completions for different meanings. In addition...

There is a strong tendency to complete a partly occluded shape. Two types of pattern completion, global and local, are frequently reported. By means of the primed-matching paradigm, it has previously been shown that global completions are prevalent for stimuli in which regularity is abundantly present. In our study the primed-matching paradigm is applied to such stimuli in order to find out whe...