Related papers: On Representational Redundancy, Surplus Structure,…
The resource theory of quantum superposition is an extension of the quantum coherent theory, in which linear independence relaxes the requirement of orthogonality. It can be used to quantify the nonclassical in superposition of finite…
We discuss the nature of structure and organization, and the process of making new Things. Hyperstructures are introduced as binding and organizing principles, and we show how they can transfer from one situation to another. A guiding…
The scattering amplitudes of planar N = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic singularities of integrands. The amplituhedron is a geometric construction of…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of $Q$-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation…
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…
The existence of least finite support is used throughout the subject of nominal sets. In this paper we give some Brouwerian counterexamples showing that constructively, least finite support does not always exist and in fact can be quite…
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…
The intended model of the homotopy type theories used in Univalent Foundations is the infinity-category of homotopy types, also known as infinity-groupoids. The problem of higher structures is that of constructing the homotopy types needed…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the…
We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate that, for unital superalgebras, all the definitions of the structure algebra and…
This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the…
By an additive structure on a hypersurface S in projective space we mean an effective action of commutative unipotent group on projective space which leaves S invariant and acts on S with an open orbit. It is known that these structures…
We prove completeness, interpolation, decidability and an omitting types theorem for certain multi dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
We present a self-contained analysis of infinity from two mathematical perspectives: set theory and algebra. We begin with cardinal and ordinal numbers, examining deep questions such as the continuum hypothesis, along with foundational…