Related papers: Independence over arbitrary sets in NSOP$_1$ theor…

Non-forking is one of the most important notions in modern model theory capturing the idea of a generic extension of a type (which is a far-reaching generalization of the concept of a generic point of a variety). To a countable first-order…

Let $R$ denote a 2-fir. The notions of F-independence and algebraic subsets of R are defined. The decomposition of an algebraic subset into similarity classes gives a simple way of translating the F-independence in terms of dimension of…

We initiate a systematic study of the class of theories without the tree property of the second kind - NTP2. Most importantly, we show: the burden is "sub-multiplicative" in arbitrary theories (in particular, if a theory has TP2 then there…

We study fragments of dependence logic defined either by restricting the number k of universal quantifiers or the width of dependence atoms in formulas. We find the sublogics of existential second-order logic corresponding to these…

We consider several conjectures on the independence of $\ell$ of the \'etale cohomology of (singular, open) varieties over $\bar{\mathbf F}_p$. The main result is that independence of $\ell$ of the Betti numbers $h^i_{\text{c}}(X,\mathbf…

In the area of Tame Geometry, different model-theoretic tameness conditions are established and their relationships are analyzed. We construct a subfield $K$ of the real numbers that lacks several of such tameness properties. As our main…

We present Gabber's theorem of independence of $l$ for the intersection cohomology of a proper equidimensional scheme over the spectrum of a finite field. We follow [Fuji] very closely. ----- On expose ici le th\'eor\`eme de Gabber…

The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operator-valued free probability. The paper presents constructions for maps with similar properties to the…

This paper considers the complexity and properties of KLM-style preferential reasoning in the setting of propositional logic with team semantics and dependence atoms, also known as propositional dependence logic. Preferential team-based…

We review some independence results in a finite axiom-schematization of classical first-order logic introduced by Norman Megill. We also prove that a certain axiom scheme of this system is independent although all of its instances are…

This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…

We present an algorithm to decide whether or not a finitely generated subgroup of the isometry group of a locally finite simplicial tree is both discrete and free. The correctness of this algorithm relies on the following conjecture: every…

In this manuscript we discuss the notion of (statistical) independence embedded in its historical context. We focus in particular on its appearance and role in number theory, concomitantly exploring the intimate connection of independence…

We give a systematic study of the model theory of generic nilpotent groups and Lie algebras. We show that the Fra\"iss\'e limit of 2-nilpotent groups of exponent $p$ studied by Baudisch is 2-dependent and NSOP$_{1}$. We prove that the class…

A prescription is presented for a new and practical correlation coefficient, $\phi_K$, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of $\phi_K$ form an advantage over…

We consider the problem of testing mutual independence among the components of a high-dimensional random vector. Building on the rank-based max-sum framework, we introduce fixed finite-$L_q$ power-sum statistics under three general classes…

This work investigates the implications of relaxing the measurement independence assumption in Bell's theorem by introducing a new class of local deterministic models that account for both particle preparation and measurement settings. Our…

Variable independence and decomposability are algorithmic techniques for simplifying logical formulas by tearing apart connections between free variables. These techniques were originally proposed to speed up query evaluation in constraint…

We introduce the notion of normal hyperimaginary and we develop its basic theory. We present a new proof of Lascar-Pillay's theorem on bounded hyperimaginaries based on properties of normal hyperimaginaries. However, the use of Peter-Weyl's…

We establish the Composition-Diamond lemma for non-associative algebras over a free commutative algebra. As an application, we prove that every countably generated non-associative algebra over an arbitrary commutative algebra $K$ can be…