Related papers: The primal framework. I
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…
Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…
We prove that a universal class categorical in a high-enough cardinal is categorical on a tail of cardinals. As opposed to other results in the literature, we work in ZFC, do not require the categoricity cardinal to be a successor, do not…
Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…
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…
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…
The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory.…
In the first part we show a counterexample to a conjecture by Shelah regarding the existence of indiscernible sequences in dependent theories (up to the first inaccessible cardinal). In the second part we discuss generic pairs, and give an…
We draw the connection between the model theoretic notions of internality and the binding group on one hand, and the Tannakian formalism on the other. More precisely, we deduce the fundamental results of the Tannakian formalism by…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
Generalizing a theorem of Campercholi, we characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures (as opposed to an elementary class). This allows us to strengthen a result of…
We give, in Sections 2 and 3, an english translation of: {\it Classes g\'en\'eralis\'ees invariantes}, J. Math. Soc. Japan, 46, 3 (1994), with some improvements and with notations and definitions in accordance with our book: {\it Class…
We study multidimensional diagrams in independent amalgamation in the framework of abstract elementary classes (AECs). We use them to prove the eventual categoricity conjecture for AECs, assuming a large cardinal axiom. More precisely, we…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
The pursuit of interpretable artificial intelligence has led to significant advancements in the development of methods that aim to explain the decision-making processes of complex models, such as deep learning systems. Among these methods,…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we…
Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key mathematical disciplines, notably homotopy…
We deal with stability theory for ``reasonable'' non-elementary classes without any remanents of compactness (like: above Hanf number or definable by L_{omega_1, omega}).