Related papers: A Higher Structure Identity Principle
Free Steiner triple systems (STS) are infinite structures that are naturally characterised by a universal property. We consider the class of free STSs from a model theoretic viewpoint. We show that free STSs on any number of generators are…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
In this paper we give an algorithm to determine, for any given suborder closed class of series-parallel posets, a structure theorem for the class. We refer to these structure theorems as structural descriptions.
Coherent information is a useful concept in quantum information theory. It connects with other notions in data processing. In this short remark, we discuss the coherent information saturating its upper bound. A necessary and sufficient…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct manner with little reliance on general coherence results. We…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
Recent discoveries have been made connecting abstract homotopy theory and the field of type theory from logic and theoretical computer science. This has given rise to a new field, which has been christened "homotopy type theory". In this…
We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…
We demonstrate, by a number of examples, that information-flow security properties can be proved from abstract architectural descriptions, that describe only the causal structure of a system and local properties of trusted components. We…
We present a comprehensive classification theory for saturated Fell bundles over locally compact groups, utilizing data associated with their base group and unit fiber. This framework offers a unified approach to understanding the structure…
We introduce a notion of globular multicategory with homomorphism types. These structures arise when organizing collections of "higher category-like" objects such as type theories with identity types. We show how these globular…
Measurability with respect to ideals is tightly connected with absoluteness principles for certain forcing notions. We study a uniformization principle that postulates the existence of a uniformizing function on a large set, relative to a…
We study models of HST, a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the language containing the membership and standardness predicates, and Saturation for well-orderable families of…
We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an…
We reformulate Hrushovski's definability patterns from the setting of first order logic to the setting of positive logic. Given an h-universal theory T we put two structures on the type spaces of models of T in two languages, \mathcal{L}…
In this paper, we provide an overview of the research conducted in the context of structural systems since the latest survey by Dion et al. in 2003. We systematically consider all the papers that cite this survey as well as the seminal work…