Related papers: Counter-examples to the minimal model theory in ch…

This is a note showing that, contrary to our lasting belief, the nonadditivity X(1+2)=X(1)+X(2)+\alpha X(1)X(2) is not a true physical property. \alpha in this expression cannot be unique for a given system. It unavoidably depends on how…

In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…

In this article I investigate the phenomenon of minimum models of second-order set theories, focusing on Kelley--Morse set theory $\mathsf{KM}$, G\"odel--Bernays set theory $\mathsf{GB}$, and $\mathsf{GB}$ augmented with the principle of…

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We reveal a contradiction in measure-theoretic probability. The contradiction is an "equation" $1/2 = 0$ with its two sides representing probabilities. Unlike known paradoxes in mathematics, the revealed contradiction cannot be explained…

We construct a weakly compact convex subset of $\ell^2$ with nonempty interior that has an isolated maximal element, with respect to the lattice order $\ell _+^2$. Moreover, the maximal point cannot be supported by any strictly positive…

A model M of cardinality lambda is said to have the small index property if for every G subseteq Aut(M) such that [Aut(M):G] <= lambda there is an A subseteq M with |A|< lambda such that Aut_A(M) subseteq G. We show that if M^* is a…

In this paper we prove a sufficient condition for the existence of matchings in arbitrary groups and its linear analogue, which lead to some generalizations of the existing results in the theory of matchings in groups and central extensions…

The Myhill isomorphism is a variant of the Cantor-Bernstein theorem. It states that, from two injections that reduces two subsets of $\mathbb{N}$ to each other, there exists a bijection $\mathbb{N} \to \mathbb{N}$ that preserves them. This…

Let P be a distinguished unary predicate and K= {M: M a model of cardinality aleph_n with P^M of cardinality aleph_0}. We prove that consistently for n=4, for some countable first order theory T we have: T has no model in K whereas every…

A theory of relative species abundance on sparsely-connected networks is presented by investigating the replicator dynamics with symmetric interactions. Sparseness of a network involves difficulty in analyzing the fixed points of the…

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

Given an invertible sheaf on a fibre space between projective varieties of positive characteristic, we show that fibrewise semi-ampleness implies relative semi-ampleness. The same statement fails in characteristic zero.

We address a recent proposal concerning 'surplus structure' due to Nguyen et al. ['Why Surplus Structure is Not Superfluous.' Br. J. Phi. Sci. Forthcoming.] We argue that the sense of 'surplus structure' captured by their formal criterion…

In this paper we prove the Lefschetz coincidence theorem in o-minimal expansions of fields using the o-minimal singular homology and cohomology.

Let $n\geq 2$ and $(X_i,1\leq i\leq n)$ be a centered Gaussian random vector. The Gaussian minimum conjecture says that $E\left(\min_{1\leq i\leq n}|X_i|\right)\geq E\left(\min_{1\leq i\leq n}|Y_i|\right)$, where $Y_1,\ldots,Y_n$ are…

In this paper we prove the central limit theorem for Hotelling's $T^2$ statistic when the dimension of the random vectors is proportional to the sample size.

We prove the following conjecture of Narayana: there are no dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime.

This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an…

Minimal model conjecture for a proper variety $X$ is that if $\kappa(X)\geq 0$, then $X$ has a minimal model with the abundance and if $\kappa =-\infty$, then $X$ is birationally equivalent to a variety $Y$ which has a fibration $Y \to Z$…