Related papers: Structural Highness Notions
Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimulin and Yamaleev. Using the same…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems…
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…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank $\omega_1^{CK}$, the computable infinitary theory is $\aleph_0$-categorical. Millar and Sacks asked whether this…
There are familiar examples of computable structures having various computable Scott ranks. There are also familiar structures, such as the Harrison ordering, which have Scott rank $\omega_1^{CK}+1$. Makkai produced a structure of Scott…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the uniqueness requirement and asks only for…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making…
Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…
We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with…
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.
We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…
The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural…
We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of…
We study the isomorphism types of simply connected complexes of rank 7/4 using a local invariant called the parity. We show that the parity can be computed explicitly in certain constructions arising from surgery.