Related papers: The strength of countable saturation
In this paper we prove a strong nonstructure theorem for kappa (T)-saturated models of a stable theory T with dop.
We argue that robustness of explanations---i.e., that similar inputs should give rise to similar explanations---is a key desideratum for interpretability. We introduce metrics to quantify robustness and demonstrate that current methods do…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
The quantum battery capacity is introduced in this letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can…
In this paper I introduce a new and intuitive first-order foundational theory (where the concept of set is not primitive) and use it to show that the power set of an infinite set does not exist. In particular, proofs of uncountability of a…
An overview is given of the theoretical work on nucleon spectral functions in finite nuclei. The consequences of the observed spectral strength distribution are then considered in the context of the nuclear-matter saturation problem.…
Coherent information is a useful concept in quantum information theory. It connects with other notions in data processing. In this short remark, we discuss the coherent information saturating its upper bound. A necessary and sufficient…
The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches…
As part of the author's studies on equational reasoning for monadic programs, this report focus on non-determinism monad. We discuss what properties this monad should satisfy, what additional operators and notations can be introduced to…
Let (G, X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of…
Several theorems on the volume computing of the polyhedron spanned by a n-dimensional vector set with the finite-interval parameters are presented and proved firstly, and then are used in the analysis of the controllable regions of the…
We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for…
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of…
The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two…
Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers.…
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…
This paper studies and proposes a technique of function point counting for items classified as non-measurable. The main objective is to expand the conventional technique of counting to ensure that this comprises consistently the tasks…
We investigate the interpretability ordering $\trianglelefteq^*$ using generalized Ehrenfeucht-Mostowski models. This gives a new approach to proving inequalities and investigating the structure of types.
In this note, we find a new way to prove several properties of 2-alternating capacities.