Related papers: Existential characterizations of monadic NIP

The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models extend to existentially closed geometric morphisms, such as…

The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…

We prove that in a countable theory $T$ fully stable over a predicate $P$, any $\lam$-complete set $A$ has the $\lam$-existence property. This means that $A$ can be extended to a $\lam$-saturated model of $T$ without changing the $P$-part.…

For a first-order formula $\phi(x;y)$ we introduce and study the characteristic sequence $<P_n : n < \omega>$ of hypergraphs defined by $P_n(y_1,...,y_n) := (\exists x) \bigwedge_{i \leq n} \phi(x;y_i)$. We show that combinatorial and…

Given a Hopf algebra in a symmetric monoidal category with duals, the category of modules inherits the structure of a monoidal category with duals. If the notion of algebra is replaced with that of monad on a monoidal category with duals…

A graph class $\mathscr{C}$ is called monadically stable if one cannot interpret, in first-order logic, arbitrary large linear orders in colored graphs from $\mathscr{C}$. We prove that the model checking problem for first-order logic is…

We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a…

Under the assumption that every material object can ultimately be described by quantum theory, we ask how a probe system evolves in a device prepared and kept in a superposition state of values of its classical parameter. We find that,…

We prove that if a separable II$_1$ factor $M$ is existentially closed, then every $M$-bimodule is weakly contained in the trivial $M$-bimodule, $\text{L}^2(M)$, and, equivalently, every normal completely positive map on $M$ is a pointwise…

We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…

The well known stability conjecture of Palis and Smale states that if a diffeomorphism is structurally stable then the chain recurrent set is hyperbolic. It is natural to ask if this type of results is true for an individual chain class,…

Mutualistic interactions, which are beneficial for both interacting species, are recurrently present in ecosystems. Observations of natural systems showed that, if we draw mutualistic relationships as binary links between species, the…

Using aritmethic conditions on affine semigroups we prove that for a simplicial toric variety of codimension 2 the property of being a set-theoretic complete intersection on binomials in characteristic $p$ holds either for all primes $p$,…

We show that for any separably closed field $k$ of characteristic $p>0$, the canonical functor from nilpotent $p$-adic spaces to $\mathbb{E}_{\infty}$-coalgebras over $k$ (given by singular chains with coefficients in $k$) is fully…

We prove that a Hopf algebra of prime dimension $p$ over an algebraically closed field, whose characteristic is equal to $p$, is either a group algebra or a restricted universal enveloping algebra. Moreover, we show that any Hopf algebra of…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.

This paper is a contribution to "neo-stability" type of result for abstract elementary classes. Under certain set theoretic assumptions, we propose a definition and a characterization of NIP in AECs. The class of AECs with NIP properly…

There exist NIP and non-NTP$_2$ theories satisfying all the following conditions: It is not o-minimal; All models are strongly locally o-minimal; It has a model which is an expansion of the linearly ordered abelian group over the reals…

We show that the computational power of the non-causal circuit model, i.e., the circuit model where the assumption of a global causal order is replaced by the assumption of logical consistency, is completely characterized by the complexity…

A first-order structure $\mathfrak{A}$ is called monadically stable iff every expansion of $\mathfrak{A}$ by unary predicates is stable. In this article we give a classification of the class $\mathcal{M}$ of $\omega$-categorical monadically…