Related papers: On categories of o-minimal structures
We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…
We prove the Zil'ber Trichotomy Principle for all 1-dimensional structures which are definable in o-minimal ones. In particular, we show that any stable 1-dimensional structure is necessarily locally modular. The main tool is a theory for…
The sole purpose of this note is to introduce some elementary results on the structure and functoriality of Reedy model categories. In particular, I give a very useful little criterion to determine whether composition with a morphism of…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
The concept of charge-transfer (CT) transitions in ferrites is based on the cluster approach and takes into account the relevant interactions as the low-symmetry crystal field, spin-orbital, Zeeman, exchange and exchange-relativistic…
We introduce the category of structures and interpretations which allows us to discuss some issues of Grothendieck's anabelian geometry in model-theory terms. Our main result is a formulation in terms of pure stability theory of a problem…
This paper introduces categories of assemblies which are closely connected to realizability interpretations and which are based on an important subcategory of the effective topos. There is a list of properties which characterize these…
Model categories have long been a useful tool in homotopy theory, allowing many generalizations of results in topological spaces to other categories. Giving a localization of a model category provides an additional model category structure…
We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from G\"ardenfors semantic spaces, categorical compositional linguistics, and…
In this article we survey some of the recent developments in the structure theory of set addition.
We give a new construction of the algebraic $K$-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and…
Ordered item response models that are in common use can be divided into three groups, cumulative, sequential and adjacent categories model. The derivation and motivation of the models is typically based on the assumed presence of latent…
We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications…
We give an example of two ordered structures M, N in the same language L with the same universe, the same order and admitting the same one-variable definable subsets such that M is a model of the common theory of o-minimal L-structures and…
In "On o-minimal homotopy groups", o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
In this article, we construct a cofibrantly generated Quillen model structure on the category of small topological categories $\mathbf{Cat}_{\mathbf{Top}}$. It is Quillen equivalent to the Joyal model structure of $(\infty,1)$-categories…
Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema…
We first extend Calder\'on's transfer principle to weighted spaces, and then we apply our results to obtain some new weighted inequalities in ergodic theory and ergodic $H^1$ spaces.