Related papers: Short proof of the Gallai-Edmonds Structure Theore…

We prove a generalizations of the Elekes-Szab\'o theorem for relations definable in strongly minimal structures that are interpretable in distal structures.

A short proof is given for the well-known Choi-Effros theorem on the structure of ranges of completely positive projections.

We present a short proof of Szemer\'edi's Theorem using a dynamical system enriched by ideas from model theory. The resulting proof contains features reminiscent of proofs based on both ergodic theory and on hypergraph regularity.

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

We provide a short proof of the 1-dimensional flat chain conjecture.

We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a…

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

In this short paper we review and extract some features of the Fredholm Alternative problem .

In this note we show that McGee's {\omega}-inconsistency result can be derived from L\"ob's theorem.

We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.

Godsil observed the simple fact that the multiplicity of 0 as a root of the matching polynomial of a graph coincides with the classical notion of deficiency. From this fact he asked to what extent classical results in matching theory…

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We prove an Erd\H{o}s--Tur\'an type inequality for compact Lie groups, from which we deduce an effective version of Deligne's equidistribution theorem.