相关论文: O-minimal cohomology: finiteness and invariance re…

We study d-minimal expansions of ordered fields, and dense pairs thereof. We also consider other generalizations of o-minimality.

The group configuration in o-minimal structures gives rise, just like in the stable case, to a transitive action of a type-definable group on a partial type. Because $acl=dcl$ the o-minimal proof is significantly simpler than Hrushovski's…

We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author's conjectures relating definably compact groups $G$…

We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…

Suppose that ${\mathcal M}$ is a model of PA and ${\mathcal N}$ is a countably generated elementary end extension of ${\mathcal M}$. Let ${\mathfrak X}$ be the set of subsets of M that are coded by ${\mathcal N}$. Then ${\mathcal M}$ has a…

We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal expansion of a real closed field, (G;+) a 2-dimensional group definable in…

We develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable…

We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity by a function definable without parameters, and that this new function can be chosen independently…

This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra…

We study a family of groups consisting of the simplest extensions of lamplighter groups. We use these groups to answer multiple open questions in combinatorial group theory, providing groups that exhibit various combinations of properties:…

We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated…

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…

In this paper we prove the Lefschetz coincidence theorem in o-minimal expansions of fields using the o-minimal singular homology and cohomology.

We analyse domination between invariant types in o-minimal expansions of ordered groups, showing that the domination poset decomposes as the direct product of two posets: the domination poset of an o-minimal expansion of a real closed…

In this paper we give an explicit characterization of o-minimal structures with definable Skolem functions/definable choice. Such structures are, after naming finitely many elements from the prime model, a union of finitely many trivial…

Termination analysis of linear loops plays a key r\^{o}le in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination…

We demonstrate that an expansion of a semi-bounded o-minimal expansion of the ordered group of reals by an increasing geometric progression is locally o-minimal.

We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…

For a group G we consider the set of natural numbers n for which the nth cohomology functor of G commutes with filtered colimit systems of coefficient modules. We find that for the large class of hierarchically decomposable groups there is…

We prove continuity results for abstract epimorphisms of locally compact groups onto finitely generated groups.