Borel's Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Emile Borel. In the 100 years since, this conjecture has led to a remarkably rich adventure of discovery in mathematics, producing independent results and the discovery of countable support iterated forcing, developments in infinitary game theory, deep connections with infinitary Ramsey Theory, and significant impact on the study of topological groups and topological covering properties. The papers in this volume present a broad introduction to the frontiers of research that has been spurred on by Borel's 1919 conjecture and identify fundamental unanswered research problems in the field. Philosophers of science and historians of mathematics can glean from this collection some of the typical trends in the discovery, innovation, and development of mathematical theories.
Borel's Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Emile Borel. In the 100 years since, this conjecture has led to a remarkably rich adventure of discovery in mathematics, producing independent results and the discovery of countable support iterated forcing, developments in infinitary game theory, deep connections with infinitary Ramsey Theory, and significant impact on the study of topological groups and topological covering properties. The papers in this volume present a broad introduction to the frontiers of research that has been spurred on by Borel's 1919 conjecture and identify fundamental unanswered research problems in the field. Philosophers of science and historians of mathematics can glean from this collection some of the typical trends in the discovery, innovation, and development of mathematical theories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and...
This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it...
A thorough introduction to Borel sets and measurable selections, acting as a stepping stone to descriptive set theory by presenting such important techniques as universal sets, prewellordering,...
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