Related papers: Separable linear orders and universality
We address a problem posed in [1] by demonstrating through an example that, in the absence of separability, the property of sequential cone compactness does not generally imply cone compactness.
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
Each linear code can be described by a code ideal given as the sum of a toric ideal and a non-prime ideal. In this way, several concepts from the theory of toric ideals can be translated into the setting of code ideals. It will be shown…
We study various orders on countably complete ultrafilters on ordinals that coincide and are wellorders under a hypothesis called the Ultrapower Axiom. Our main focus is on the relationship between the Ultrapower Axiom and the linearity of…
Following on from the notion of (first-order) causality, which generalises the notion of being tracepreserving from CP-maps to abstract processes, we give a characterization for the most general kind of map which sends causal processes to…
Semantics of a sentence is defined with much less ambiguity than semantics of a single word, and we assume that it should be better preserved by translation to another language. If multilingual sentence embeddings intend to represent…
Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types.…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
We believe we have made progress in the age-old problem of divisibility rules for integers. Universal divisibility rule is introduced for any divisor in any base number system. The divisibility criterion is written down explicitly as a…
We study supersolvable line arrangements in ${\mathbb P}^2$ over the reals and over the complex numbers, as the first step toward a combinatorial classification. Our main results show that a nontrivial (i.e., not a pencil or near pencil)…
It has long been noticed that high dimension data exhibits strange patterns. This has been variously interpreted as either a "blessing" or a "curse", causing uncomfortable inconsistencies in the literature. We propose that these patterns…
It is known that the set of tautologies of second order intuitionistic propositional logic, $\mathrm{IPC} 2$, is undecidable. Here, we prove that the sets of formulas of $\mathrm{IPC} 2$ which are true in the algebra of open subsets of…
Supervised machine learning models boast remarkable predictive capabilities. But can you trust your model? Will it work in deployment? What else can it tell you about the world? We want models to be not only good, but interpretable. And yet…
We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.
We give a criterion when an expansion of the ordered set of real numbers defines the image of the expansion of the real field by the set of natural numbers under a semialgebraic injection. In particular, we show that for a non-quadratic…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
For each integer $m \geq 2$, a network is constructed which is solvable over an alphabet of size $m$ but is not solvable over any smaller alphabets. If $m$ is composite, then the network has no vector linear solution over any $R$-module…
A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.
We give a closed formula for the dimension of all linear systems in $\mathbb{P}^n$ with assigned multiplicity at arbitrary collections of points lying on a rational normal curve of degree $n$. In particular we give a purely geometric…
In this paper, we introduce the notion of circular orderability for quandles. We show that the set all right (respectively left) circular orderings of a quandle is a compact topological space. We also show that the space of right…