Related papers: A note on NSOP$_{1}$ in one variable

Using monotonicity theory we investigate the continuous dependence on parameters for the discrete BVPs which can be written in a form of a nonlinear system.

We apply the recently developed technology of cofinality spectrum problems to prove a range of theorems in model theory. First, we prove that any model of Peano arithmetic is $\lambda$-saturated iff it has cofinality $\geq \lambda$ and the…

In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.

In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…

We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.

A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…

We prove that there is an absolute constant $C>0$ so that for every natural $n$ there exists a triangle-free \emph{regular} graph with no independent set of size at least $C\sqrt{n\log n}$.

In several articles, this author has advocated an alternative approach towards quantum foundation based upon a set of postulates, and based upon the notions of theoretical variables and of accessible theoretical variables. It is shown in…

Forking is a central notion of model theory, generalizing linear independence in vector spaces and algebraic independence in fields. We develop the theory of forking in abstract, category-theoretic terms, for reasons both practical (we…

We propose a test of the significance of a variable appearing on the Lasso path and use it in a procedure for selecting one of the models of the Lasso path, controlling the Family-Wise Error Rate. Our null hypothesis depends on a set A of…

The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for…

We prove that the first order theory of nonabelian free groups eliminates the "there exists infinitely many" quantifier (in eq). Equivalently, since the theory of nonabelian free groups is stable, it does not have the finite cover property.…

We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…

It is known that if X is uniformly distributed modulo 1 and Y is an arbitrary random variable independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable…

We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.

Suppose that $A \subset \{1,\dots, N\}$ has no two elements differing by $p-1$, $p$ prime. Then $|A| \ll N^{1 - c}$.

We characterize model theoretic properties of the Urysohn sphere as a metric structure in continuous logic. In particular, our first main result shows that the theory of the Urysohn sphere is $\text{SOP}_n$ for all $n\geq 3$, but does not…

We adapt the properties of Kim-independence in NSOP1 theories with existence proven in [5],[4] and [2] by Ramsey, Kaplan, Chernikov, Dobrowolski and Kim to hyperimaginaries by adding the assumption of existence for hyperimaginaries. We show…

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…