Related papers: Reflection principles, GCH and the uniformization …
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals' uniformity numbers can be pairwise different. In addition we show that, in the…
We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e.…
We propose a reflection principle for holomorphic objects in ${\Bbb C}^n$. Our construction generalizes the classical principle of H.Lewy, S.Pinchuk and S.Webster.
We examine the Zermelo Fraenkel set theory with Choice (ZFC) enhanced by one of the (structural) reflection principles down to a small cardinal and/or Recurrence Axioms defined below. The strongest forms of reflection principles spotlight…
We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting…
The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and…
Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity…
We study three kinds of compactness in some variants of G\"odel logic: compactness, entailment compactness, and approximate entailment compactness. For countable first-order underlying language we use the Henkin construction to prove the…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
In a recent experiment, the out-of-plane surface susceptibility of a single-layer two-dimensional atom crystal in the visible spectrum has been measured. This susceptibility gives a measurable contribution to the reflectivity of…
We study two properties for subsets of a metric space. One of them is generalization of chainability, finite chainability, and Menger convexity for metric spaces; while the other is a generalization of compactness. We explore the basic…
We report a unified representation of the spatial and angular Goos-Hanchen and Imbert-Fedorov shifts that occur when a light beam reflects from a plane interface. We thus reveal the dual nature of spatial and angular shifts in optical beam…
Based on the generalized uncertainty principle (GUP), proposed by some approaches to quantum gravity such as string theory and doubly special relativity theories, we investigate the effect of GUP on the thermodynamic properties of compact…
This paper proposes an analysis of the effects of consensus and preference aggregation on the consistency of pairwise comparisons. We define some boundary properties for the inconsistency of group preferences and investigate their relation…
The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents' decision-making. Reflexion is considered as agent's beliefs about nature, opponents' beliefs…
There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles.…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…