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Book DetailsContemporary MathematicsVolume: 755; 2020; 242 ppMSC: Primary 03; 22; 54; 91
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 Émile 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.
ReadershipGraduate students and research mathematicians interested in topology, set theory, and infinitary Ramsey theory.
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Table of Contents
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Articles
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Leandro F. Aurichi and Rodrigo R. Dias — Game-theoretical aspects of the Borel conjecture
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Michael Hrušák and Ondřej Zindulka — Strong measure zero in Polish groups
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Marion Scheepers — Ramsey theory and the Borel conjecture
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Tomasz Weiss — On the algebraic union of strongly measure zero sets and their relatives with sets of real numbers
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Wolfgang Wohofsky — Borel Conjecture, dual Borel Conjecture, and other variants of the Borel Conjecture
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Lyubomyr Zdomskyy — Selection principles in the Laver, Miller, and Sacks models
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Additional Material
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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 Émile 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.
Graduate students and research mathematicians interested in topology, set theory, and infinitary Ramsey theory.
-
Articles
-
Leandro F. Aurichi and Rodrigo R. Dias — Game-theoretical aspects of the Borel conjecture
-
Michael Hrušák and Ondřej Zindulka — Strong measure zero in Polish groups
-
Marion Scheepers — Ramsey theory and the Borel conjecture
-
Tomasz Weiss — On the algebraic union of strongly measure zero sets and their relatives with sets of real numbers
-
Wolfgang Wohofsky — Borel Conjecture, dual Borel Conjecture, and other variants of the Borel Conjecture
-
Lyubomyr Zdomskyy — Selection principles in the Laver, Miller, and Sacks models
