相关论文: The Banach-Tarski Paradox

The classical logical antinomy known as Richard-Berry paradox is combined with plausible assumptions about the size i.e. the descriptional complexity of Turing machines formalizing certain sentences, to show that formalization of language…

Being motivated by the famous Kaplansky theorem we study various sequential properties of a Banach space $E$ and its closed unit ball $B$, both endowed with the weak topology of $E$. We show that $B$ has the Pytkeev property if and only if…

This is an epistemological approach to errors in both inference and risk management, leading to necessary structural properties for the probability distribution. Many mechanisms have been used to show the emergence of fat tails. Here we…

We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…

While exploring dynamical systems, we often come across the principle of contraction mapping, or better known as the Banach fixed point theorem. It is an essential concept based on successive approximation, whose utility comes from two main…

Banaszczyk's inequality establishes a tail estimate for the discrete Gaussian measure on a lattice in $\mathbb{R}^n$. This classic result has been influential and plays an important role in lattice-based cryptography. An improvement of the…

The clock paradox is analyzed for the case when the onward and return trips cover the same <<distance>> (as observed by the traveling twin) but at unequal velocities. In this case the stationary twin observes the distances covered by her…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

A Banach space has the Schur property when every weakly convergent sequence converges in norm. We prove a Schur-like property for measures: if a sequence of finite signed Borel measures on a Polish space is such that it is bounded in total…

``No one has ever touched Zeno without refuting him''. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science. The paper begins with a brief biography of Zeno of Elea followed by his…

The concept of presence has been extensively explored in philosophy, yet the notion of particle presence within quantum theory remains under-examined. In this article, we explore particle presence through an analysis of a paradox arising…

Hardy's paradox was originally presented as a demonstration, without inequalities, of the incompatibility between quantum mechanics and the hypothesis of local causality. Equipped with newly developed tools that allow for a quantitative…

Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.

Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…

Hausdorff's gap condition was satisfied by his original 1936 construction of an (omega-1,omega-1) gap in P(N)/Fin. We solve an open problem in determining whether Hausdorff's condition is actually stronger than the more modern…

We consider the well-posedness of Bayesian inverse problems when the prior measure has exponential tails. In particular, we consider the class of convex (log-concave) probability measures which include the Gaussian and Besov measures as…

We investigate several possibilities of obtaining a {\L}ojasiewicz inequality for definable multifunctions and give some examples of applications thereof. In particular, we prove that the Hausdorff distance and its extension to closed sets…

The special theory of relativity is the foundation of modern physics, but its unusual postulate of invariant vacuum speed of light results in a number of plausible paradoxes. This situation leads to radical criticisms and suspicions against…

In this note it is proved that the class of paratopologies is simple and that under the assumption that the measurable cardinals form a proper class, the class of hypotopologies is not simple. Moreover, an example is given of a Hausdorff…

This article reads the four paradoxes mechanised in the coq-paradoxes package, namely the Burali-Forti paradox in system U, the Diaconescu paradox that the axiom of choice entails excluded middle, the Reynolds paradox that System F has no…