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Hausdorff on Ordered Sets
Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem in his famous Paris lecture. It was time for the appearance of the second generation of Cantorians. They emerged in the decade 1900-1909, and foremost among them were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and pursued set theory as part of the mathematical arsenal. He was recognized as the era's leading Cantorian. From 1901-1909, Hausdorff published seven articles in which he created a representation theory for ordered sets and investigated sets of real sequences partially ordered by eventual dominance, together with their maximally ordered subsets. These papers are translated and appear in this volume. Each is accompanied by an introductory essay. These highly accessible works are of historical significance, not only for set theory, but also for model theory, analysis and algebra.
Jews and Sciences in German Contexts
The authors examine the relationship between the cultural, religious and social situation of German Jews on the one hand and their scientific activities on the other. They discuss the sensitive question of the specificity of the approaches of Jewish scientists and draw attention to the debate concerning the relationship between Judaism and academic research, ranging from the early 19th century theorizing on science and Judaism to 20th century issues, e.g. the controversies on 'Jewish' physics, mathematics etc. in the 1920s and 30s. Contributors: Ute Deichmann, Anthony S. Travis, Moritz Epple, Raphael Falk, Ulrich Charpa, Nurit Kirsch, Yael Hashiloni-Dolev, Aharon Loewenstein, Ruth Sime, Simone Wenkel
Sitzungsberichte der Berliner Mathematischen Gesellschaft
List of members in 2.- Jahrg.
The Theory of Models
Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders ...
Institutions and Applications
The History of Modern Mathematics, Volume II: Institutions and Applications focuses on the history and progress of methodologies, techniques, principles, and approaches involved in modern mathematics. The selection first elaborates on crystallographic symmetry concepts and group theory, case of potential theory and electrodynamics, and geometrization of analytical mechanics. Discussions focus on differential geometry and least action, intrinsic differential geometry, physically-motivated research in potential theory, introduction of potentials in electrodynamics, and group theory and crystallography in the mid-19th century. The text then elaborates on Schouten, Levi-Civita, and emergence of ...
Mathematical Reviews
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Zahlen, Zeichen und Figuren
Der Sammelband fragt nach dem Verhältnis zwischen der Mathematik und den schönen Künsten vom Mittelalter bis in die Gegenwart. Untersucht wird der Einfluss mathematischer Wissensordnungen, Quantifizierungs-, Formalisierungs- und Abstraktionsverfahren auf das musikalische, bildkünstlerische und poetische Schaffen. Aus der Fülle der herangezogenen historischen Paradigmen wird deutlich, dass die Bereitschaft der Komponisten, Künstler und Dichter, sich durch die Eigentümlichkeit der Mathematik herausfordern und ästhetisch inspirieren zu lassen, viel größer war als gemeinhin angenommen wird. Im Vordergrund der Beiträge stehen einerseits thematische Reflexionen des Mathematischen in Kun...
