Related papers: On the model theory of open generalized polygons

This work is dedicated to the results were got in the model theory of the regular polygons. We give the characterization of the monoids with axiomatizable and model complete class of regular polygons. We describe the monoids with complete…

We prove that each \omega-categorical, generically stable group is solvable-by-finite.

We characterize stable T for which the model completion of T_{aut} is stable (i.e., every completion is). Then we prove that ``some completion is stable'' is different and we characterize it. Finally we show that if T is stable, T_{aut} has…

A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…

We prove that, if $n\geq 3$, a singular foliation $\mathcal{F}$ on $\mathbb P^n$ which can be written as pull-back, where $\mathcal{G}$ is a foliation in $ {\mathbb P^2}$ of degree $d\geq2$ with one or three invariant lines in general…

Adapting a proof of Bouscaren and Delon, we show that every type-definable connected group in a given stable theory of fields embeds into an algebraic group, under a condition on the definable closure. We also present general hypotheses…

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

We prove that the stably free modules over a smooth affine threefold over an algebraically closed field of characteristic different from 2 are free.

We classify families of free rational curves on all smooth Fano threefolds over the complex numbers. In particular, we prove the family of very free rational curves representing any fixed numerical curve class is either irreducible or…

We initiate a systematic study of \emph{generic stability independence} and introduce the class of \emph{treeless theories} in which this notion of independence is particularly well-behaved. We show that the class of treeless theories…

We prove that every stable Hamiltonian structure on a closed oriented three-manifold is stably homotopic to one which is supported (with suitable signs) by an open book.

A complete first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition.…

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…

We prove that if K is an infinite stable field whose generic type has weight 1 then K is separably closed. We also obtain partial results when the generic of K has finite weight and when K is strongly stable.

We prove that the irreducible decomposition of the permutation representation of GL(n,q) on GL(n,q)/GL(n-m,q) stabilizes for large n. We deduce, as a consequence, a representation stability theorem for finitely generated VIC-modules.

We examine a class of geometric theorems on cyclic 2n-gons. We prove that if we take n disjoint pairs of sides, each pair separated by an even number of polygon sides, then there is a linear combination of the angles between those sides…

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…

We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra…

We use the theory of resultants of polynomials to study the stability of an arbitrary polynomial over a finite field, that is, the property of having all its iterates irreducible. This result partially generalises the quadratic polynomial…