Related papers: Coherent Adequate Sets and Forcing Square
We extend the notion of exact completion on a weakly lex category to elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which freely adds effective quotients and extensional equality. We note that…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
This paper presents a new framework for constructing congruence closure of a finite set of ground equations over uninterpreted symbols and interpreted symbols for the group axioms. In this framework, ground equations are flattened into…
This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.
The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set…
The purpose of this article is to give a presentation of the method of forcing aimed at someone with a minimal knowledge of set theory and logic. The emphasis will be on how the method can be used to prove theorems in ZFC.
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
Given a finite subset of a sphere or projective space, known as a design, we can compute the strength and angle set of that design. When the strength and angle set meet certain bounds, the design is called tight. Hoggar sought to prove…
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…
We propose a calculus for modeling implicit programming that supports first-class, overlapping, locally scoped, and higher-order instances with higher-kinded types. We propose a straightforward generalization of the well-established System…
Given a Polish space X and a countable family of analytic hypergraphs on X, I consider the sigma-ideal generated by Borel sets which are anticliques in at least one hypergraph in the family. It turns out that many of the quotient posets are…
An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For…
In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
This study delves into equilibrium problems, focusing on the identification of finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium…
Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…
These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…
Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…