Related papers: Existential characterizations of monadic NIP

A profinite group G is just infinite if every non-trivial closed normal subgroup of G is of finite index, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups need not be…

A character (ordinary or modular) is called orthogonally stable if all non-degenerate quadratic forms fixed by representations with those constituents have the same determinant mod squares. We show that this is the case provided there are…

Let $T$ be a consistent o-minimal theory extending the theory of densely ordered groups and let $T'$ be a consistent theory. Then there is a complete theory $T^*$ extending $T$ such that $T$ is an open core of $T^*$, but every model of…

This paper provides a full characterization for when the expansion of a complete o-minimal theory by a unary predicate that picks out a divisible dense and codense subgroup has a model companion. This result is motivated by criteria and…

As it was argued by Anderson [Science 177, 393 (1972)], the "reductionist" hypothesis does not by any means imply a "constructionist" one. Hence, in general, the behavior of large and complex aggregates of elementary components can not be…

Let $f(x)\in {\mathbb Z}[x]$ be monic of degree $N\ge 2$. Suppose that $f(x)$ is monogenic, and that $f(x)$ is the characteristic polynomial of the $N$th order linear recurrence sequence $\Upsilon_f:=(U_n)_{n\ge 0}$ with initial conditions…

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e. with a ghost. We prove analytically that the classical motion of the system is completely…

We show that $\omega$-categorical rings with NIP are nilpotent-by-finite. We prove that an $\omega$-categorical group with NIP and fsg is nilpotent-by-finite. We also notice that an $\omega$-categorical group with at least one strongly…

We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.

Suppose that M is an infinite structure with finite relational vocabulary such that every relation symbol has arity at most 2. If M is simple and homogeneous then its complete theory is supersimple with finite SU-rank which cannot exceed…

In this short paper we prove that a finite dimensional algebra is hereditary if and only if there is no loop in its ordinary quiver and every $\tau$-tilting module is tilting.

A visceral structure on M is given by a definable base for a uniform topology on its universe in which all basic open sets are infinite and any infinite definable subset X of M has non-empty interior. This context includes o-minimal ordered…

We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…

We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets. For a fixed number of 4-types, we show that there are only finitely many such structures and that all are built out of finitely…

Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…

Let $\ell^p$ be the space of all $p$-summable sequences on $\mathbb{Z}$. An infinite matrix is said to have $\ell^p$-stability if it is bounded and has bounded inverse on $\ell^p$. In this paper, a practical criterion is established for the…

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…

We present a structural approach of some results about jumps in the behavior of the profile (alias generating function) of hereditary classes of finite structures. We consider the following notion due to N.Thi\'ery and the second author. A…

Let $K$ be an NIP field and let $v$ be a henselian valuation on $K$. We ask whether $(K,v)$ is NIP as a valued field. By a result of Shelah, we know that if $v$ is externally definable, then $(K,v)$ is NIP. Using the definability of the…

Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane have uniformly perfect attractor sets, while other conditions imply the attractor is pointwise thin, and thus…