Related papers: Definable Groups in DCFA
An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik-Chervonenkis density. Furthermore, strong abelian groups are…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
An integral of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. In this paper, we prove that the integrability of a finite group is a decidable problem.
We prove the definability, and actually the finiteness of the commutator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable…
The concept of configuration was first introduced by Rosenblatt and Willis to give a characterization for the amenability of groups. We show that group properties of being soluble or FC can be characterized by configuration sets. Then we…
In this work, we classify the group gradings on finite-dimensional incidence algebras over a field, where the field has characteristic zero, or the characteristic is greater than the dimension of the algebra, or the grading group is…
Previous formulations of group theory in ACL2 and Nqthm, based on either "encapsulate" or "defn-sk", have been limited by their failure to provide a path to proof by induction on the order of a group, which is required for most interesting…
We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in…
We introduce characteristic numbers of a finite commutative unital $\mathbb{C}$-algebra, which are numerical invariants arising from algebraic intersection theory. We characterize Gorenstein and local complete intersection algebras in terms…
The formal class of a germ of diffeomorphism $\phi$ is embeddable in a flow if $\phi$ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at…
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…
We develop the nonuniformly hyperbolic theory for $C^1$ diffeomorphisms admitting continuous invariant splitting without domination. This framework includes stable manifold theorems, shadowing and closing lemmas, the existence of horseshoes…
We consider interpretable topological spaces and topological groups in a $p$-adically closed field $K$. We identify a special class of "admissible topologies" with topological tameness properties like generic continuity, similar to the…
In this paper we study definable families of functions from an ordered abelian group into various naturally arising definable quotients. We show that for an ordered abelian group $G$ and definable family of convex subgroups…
We reformulate Hrushovski's definability patterns from the setting of first order logic to the setting of positive logic. Given an h-universal theory T we put two structures on the type spaces of models of T in two languages, \mathcal{L}…
We demonstrate that topological defects in a rational conformal field theory can be described by a classifying algebra for defects - a finite-dimensional semisimple unital commutative associative algebra whose irreducible representations…
Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…
The text is based on notes from a class entitled {\em Model Theory of Berkovich Spaces}, given at the Hebrew University in the fall term of 2009, and retains the flavor of class notes. It includes an exposition of material from…
We develop the theory of continuous and algebraic domains in constructive and predicative univalent foundations, building upon our earlier work on basic domain theory in this setting. That we work predicatively means that we do not assume…
This article discusses the modular representation theory of finite groups of Lie type from the viewpoint of Broue's abelian defect group conjecture. We discuss both the defining characteristic case, the inspiration for Alperin's weight…