Related papers: On the infinitary van der Waerden Theorem

A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.

Extending Sellers' result, Das et al. recently proved some congruence results for generalized overcubic partitions using theta functions and posed some related conjectures. In this paper, we provide a combinatorial proof of a result in…

In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953.…

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

We present a proof of completeness for the implicational propositional calculus, based on a variant of the Lindenbaum procedure.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

I give a proof of the confluence of combinatory strong reduction that does not use the one of lambda-calculus. I also give simple and direct proofs of a standardization theorem for this reduction and the strong normalization of simply typed…

By using a general formalism, we expose a simplified proof of the convergence of the B\'ezier polynomials attached to a continuous function defined in arbitrary dimensional simplex. We obtain an error estimate that contains the error in…

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.

We prove a uniform vector-valued Wiener-Wintner Theorem for a class of operators that includes compositions of ergodic Koopman operators with contractive multiplication operators. Our results are new even in the case of complex-valued…

Solving a problem of Diestel and Pott, we construct a large class of infinite matroids. These can be used to provide counterexamples against the natural extension of the Well-quasi-ordering-Conjecture to infinite matroids and to show that…

We relate extensions of completely unitary VOAs and (commutative) Q-systems. As an application, we show that any unitary extension of a completely unitary VOA is completely unitary.

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

We prove some theorems on decomposable continua. In particular, we prove; (i) the property of being a Wilder continuum is not a Whitney reversible property, (ii) inverse limits of D**-continua with surjective monotone upper semi-continuous…

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

We give a proof for the decidability of the HD0L ultimate periodicity problem.

We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.