Related papers: How to take cats together

Enlarging on Parts I and II we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of full dynamic equations, including equations where the medium is moving or otherwise changing…

This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: {\sf All $x$ are $y$} and {\sf Some $x$ are…

Dialectica categories are a very versatile categorical model of linear logic. These have been used to model many seemingly different things (e.g., Petri nets and Lambek's calculus). In this note, we expand our previous work on fuzzy petri…

A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…

We prove that the definition of supersimplicity in metric structures from \cite{pezz:Morley} is equivalent to an \textit{a priori} stronger variant. This stronger variant is then used to prove that if $T$ is a supersimple Hausdorff cat then…

Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…

Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine…

We study the extension of dependence logic D by a majority quantifier M over finite structures. We show that the resulting logic is equi-expressive with the extension of second-order logic by second-order majority quantifiers of all…

There exist two known canonical types of ultrafilter extensions of first-order models; one comes from modal logic and universal algebra, another one from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as…

Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…

The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…

We introduce the theory of generalised ultracategories, these are relational extensions to ultracategories as defined by Lurie. An essential example of generalised ultracategories are topological spaces, and these play a fundamental role in…

Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…

Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…

In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…

Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…

We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…

This paper introduces and defends an account of model-based science that I dub model pluralism. I argue that despite a growing awareness in the philosophy of science literature of the multiplicity, diversity, and richness of models and…

We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…

Taking symmetric extensions can be considered as a generalisation of forcing, which produces a richer multiverse of models with and without the axiom of choice. We can study the structure of this multiverse using modal logic. In particular,…