Related papers: The Univalence Principle
Understanding how particles are arranged on the sphere is not only central to numerous physical, biological, and materials systems but also finds applications in mathematics and in analysis of geophysical and meteorological measurements. In…
In this paper we prove equivalence of sets of axioms for non-discrete affine buildings, by providing different types of metric, exchange and atlas conditions. We apply our result to show that the definition of a Euclidean building depends…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
In their usual form, representation independence metatheorems provide an external guarantee that two implementations of an abstract interface are interchangeable when they are related by an operation-preserving correspondence. If our…
We prove undecidability for every positive relevant logic extending the system axiomatized by hypothetical syllogism, prefixing, and suffixing and contained in the logic of the semilattice frame $(P_{\mathrm{fin}}(\mathbb{N}), \cup,…
The uniform continuity theorem (UCT) states that every pointwise continuous real-valued function on the unit interval is uniformly continuous. In constructive mathematics, UCT is stronger than the decidable fan theorem (DFT); however, Loeb…
In this note we present a notion of fundamental scheme for Cohen- Macaulay, order 1, irreducible congruences of lines. We show that such a congruence is formed by the k-secant lines to its fundamental scheme for a number k that we call the…
In this paper, we consider a model of classical linear logic based on coherence spaces endowed with a notion of totality. If we restrict ourselves to total objects, each coherence space can be regarded as a uniform space and each linear map…
Uninorms play a prominent role both in the theory and the applications of Aggregations and Fuzzy Logic. In this paper the class of group-like uninorms is introduced and characterized. First, two variants of a general construction -- called…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure $M$. We prove that if $T$ is a complete $L$-theory, then $T$ is mutually algebraic if and only if there is some model $M$ of $T$ for…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
We describe a construction process of a relevant measure in any non-empty compact metric space. This probability measure has invariance properties with respect to isometric maps defined on open sets. These properties imply that this measure…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as `bridges' for…
For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger and Kleiner paper arXiv:math/0611954 and…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…