Related papers: On structures in hypergraphs of models of a theory
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
Multi-layer graphs can capture qualitatively different types of connection between entities, and networks of this kind are prevalent in biological and social systems: for example, a social contact network typically involves both virtual and…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an…
This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…
In this paper we define some ballean structure on the power set of a group and, in particular, we study the subballean with support the lattice of all its subgroups. If $G$ is a group, we denote by $L(G)$ the family of all subgroups of $G$.…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
The topology of the band structure, which is determined by the lattice symmetries, has a strong influence on the transport properties. Here we consider an anisotropic honeycomb lattice and study the effect of a continuously deformed band…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
Suppose $X$ is a locally solid lattice ring. It is known that there are three classes of bounded group homomorphisms on $X$ whose topological structures make them again topological rings. In this note, we consider lattice structure on them;…
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…
The study of homotopy theoretic phenomena in the language of type theory is sometimes loosely called `synthetic homotopy theory'. Homotopy theory in type theory is only one of the many aspects of homotopy type theory, which also includes…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
"Theory figures" are a staple of theoretical visualization research. Common shapes such as Cartesian planes and flowcharts can be used not only to explain conceptual contributions, but to think through and refine the contribution itself.…
Structuring theories is one of the main approaches to reduce the combinatorial explosion associated with reasoning and exploring large theories. In the past we developed the notion of development graphs as a means to represent and maintain…
Two main topics are considered: The characterisation of finite homomorphism dualities for relational structures, and the splitting property of maximal antichains in the homomorphism order.
We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to…