Related papers: Toward categoricity for classes with no maximal mo…

We prove a main gap theorem for e-saturated submodels of a homogeneous structure. We also study the number of e-saturated models, which are not elementarily embeddable to each other

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

We construct an abstract elementary class $K_1$ of torsion-free abelian groups such that $K_1$ is not $(<\aleph_0)$-tame but is $\aleph_0$-tame. This answers a question of [BoVa17]. Furthermore, for every regular uncountable cardinal $\mu$…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

We put in print a classical result that states that for most purposes, there is no harm in assuming the existence of saturated models in model theory. The presentation is aimed for model theorists with only basic knowledge of axiomatic set…

Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…

Many counterexamples are known in the class of small theories due to Goncharov and Millar. The prime model of a decidable small theory is not necessarily decidable. The saturated model of a hereditarily decidable small theory is not…

$\mu$-Abstract Elementary Classes are a model theoretic framework introduced in [BGL+16] to encompass classes axiomatized by $\mathbb{L}_{\infty, \infty}$. We show that the framework extends beyond these logics by showing classes…

We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of $M$ arbitrary training classifiers. If the classifiers are consistent,…

Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…

We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…

This work presents a new strategy for multi-class classification that requires no class-specific labels, but instead leverages pairwise similarity between examples, which is a weaker form of annotation. The proposed method, meta…

In contrast to conventional (single-label) classification, the setting of multilabel classification (MLC) allows an instance to belong to several classes simultaneously. Thus, instead of selecting a single class label, predictions take the…

The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations…

We try to build, provably in ZFC, for a first order T a model in which any isomorphism between two Boolean algebras is definable. The problem, compared to [Sh:384], is with pseudo-finite Boolean algebras. A side benefit is that we do not…

We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of…

In the framework of graphs, we study abstract elementary classes (aecs). In this work we analyze several properties of Forb(G) and versions of Forb-Con(G) in the context of aecs and we present some examples of classes of graphs which…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

Let 2<n\leq l<m< \omega. Let L_n denote first order logic restricted to the first n variables. We show that the omitting types theorem fails dramatically for the n--variable fragments of first order logic with respect to clique guarded…