Related papers: Invariant Keisler measures for omega-categorical s…

In the present paper we shall prove that countable \omega-categorical simple CM-trivial theories and countable \omega-categorical simple theories with strong stable forking are low. In addition, we observe that simple theories of bounded…

This paper provides two extensions of first order logic by `$\omega$-rules'. In each case we characterize the countable structures whose theory in the logic is categorical (has a unique model). In the one-sorted inferential $\omega$-logic,…

J. Zapletal asked if all the forcing notions considered in his monograph are homogeneous. Specifically, he asked if the forcing consisting of Borel sets of $\sigma$-finite 2-dimensional Hausdorff measure in $\mathbb{R}^3$ (ordered under…

Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform…

We build on the results of [6] to show that the homology groups $\mathrm{H}_{r_1+r_2}(Y_0(\mathcal{N}_\Sigma),\mathcal{O})_{\mathfrak{m}_\Sigma}$ of arithmetic manifolds are free over certain deformation rings $R_\Sigma$, when there are…

In this paper, the concept of weakly uniform perfectness is considered. As an analogue of the theory of uniform perfectness, we obtain the relationships between weakly uniform perfectness and Bergman kernel, Poincar\'e metric and Hausdorff…

In the context of metric structures introduced by Ben Yaacov, Berenstein, Henson, and Usvyatsov, we exhibit an explicit encoding of metric structures in countable signatures as pure metric spaces in the empty signature, showing that such…

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

For a class of irrational numbers, depending on their Diophantine properties, we construct explicit rank-one transformations that are totally ergodic and not weakly mixing. We classify when the measure is finite or infinite. In the finite…

We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal $\mathcal{SN}$. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which…

We provide a condition on a set of directions $\Omega \subset \mathbb{S}^1$ ensuring that the associated directional maximal operator $M_\Omega$ is unbounded on $L^p(\mathbb{R}^2)$ for every $1 \leq p < \infty$. The techniques of proof…

Taking inspiration from [1, 21, 24], we develop a general framework to deal with the model theory of open incidence structures. In this first paper we focus on the study of systems of points and lines (rank $2$). This has a number of…

We extend Mazzola's counterpoint model using category theory, generalizing from the category $\mathbf{Set}$ to other topoi with suitable properties. This generalization suggests that counterpoint's essential structure depends on specific…

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…

We prove that every many-sorted $\omega$-categorical theory is completely interpretable in a one-sorted $\omega$-categorical theory. As an application, we give a short proof of the existence of non $G$--compact $\omega$-categorical…

Let $K \subset \mathbb{R}^{2}$ be a rotation and reflection free self-similar set satisfying the strong separation condition, with dimension $\dim K = s > 1$. Intersecting $K$ with translates of a fixed line, one can study the $(s -…

We prove that a singular part $\mu_s$ of a measure $\mu$ satisfying ${\cal A}\mu =0$ for a linear partial differential operator ${\cal A}$ defined on $R^d$ has the range in the intersection of kernels of the principal symbol of ${\cal A}$…

We generalize Hrushovski's Group Configuration Theorem to quasiminimal classes. As an application, we present Zariski-like structures, a generalization of Zariski geometries, and show that a group can be found there if the pregeometry…

Menger's conjecture that Menger spaces are /sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polish spaces. For non-metrizable spaces, analytic Menger spaces…

We construct logistic maps whose restriction to the omega-limit set of its critical point is a minimal Cantor system having a prescribed number of distinct ergodic and invariant probability measures. In fact, we show that every metrizable…