Ernst Zermelo : an approach to his life and work. In cooperation with Volker Peckhaus

Gebundene ORIGINALAUSGABE, kein billiger print-on-demand, bestens erhalten, keinerlei Gebrauchsspuren.Berlin 1871-1897 1 1.1 Family and Youth 1 1.2 School and University Studies 5 1.3 Ph. D. Thesis and the Calculus of Variations 10 1.4 The Boltzmann Controversy 15 1.4.1 The Situation 15 1.4.2 The First Round 17 1.4.3 The Second Round 21 1.4.4 After the Debate 23 Gottingen 1897-1910 27 2.1 Introduction 27 2.2 Working in Applied Mathematics 28 2.2.1 Habilitation 29 2.2.2 Applied Mathematics After the Habilitation 32 2.3 First Years as a Privatdozent in Gottingen 33 2.3.1 Privatdozenten Grant and Titular Professorship 33 2.3.2 Under Consideration in Breslau 1903 34 2.4 The Context: Hilbert's Research on Foundations 36 2.4.1 Mathematical Problems and Foundations 36 2.4.2 Foundations of Geometry and Analysis 40 2.4.3 The Paradoxes 41 2.5 Starting Set Theory ., 47 2.5.1 Zermelo's First Period of Foundational Research 47 2.5.2 Early Work 48 2.5.3 The Heidelberg Congress 1904 50 2.6 Zermelo's First Well-Ordering Proof 53 2.6.1 The Proof and its Motivation 53 2.6.2 Reactions 59 2.7 Finite Sets v 61 2.8 The New Proof Paper . . .' 2.8.1 Zermelo's Defence 65 2.8.2 The New Proof 69 2.8.3 Toward Acceptance of the Axiom of Choice 70 2.8.4 Postscriptum: Zermelo and Bernstein 72 2.9 The Axiomatization of Set Theory 76 2.9.1 Motivations 76 2.9.2 The Axiom System 79 2.9.3 Dedekind's Influence 84 2.9.4 The Axiom of Separation 86 2.9.5 The Range of the Axioms 89 2.9.6 Reception of the Axiom System 91 2.10 The Institutionalization of Mathematical Logic 92 2.10.1 Zermelo's Lectureship for Mathematical Logic 92 2.10.2 The 1908 Course "Mathematische Logik" 96 2.10.3 Hilbert and Zermelo 102 2.11 Waiting for a Professorship 105 2.11.1 Deterioration of Health 105 2.11.2 Wiirzburg 1906 106 2.11.3 Wiirzburg 1909 107 2.11.4 An Extraordinary Professorship Ill Zurich 1910-1921 113 3.1 A Full Professorship 113 3.1.1 Legends 113 3.1.2 The Chair in Zurich 114 3.1.3 Under Consideration at the Technical University of Breslau 117 3.1.4 Zermelo's Medical History 119 3.1.5 The End of Zermelo's Career 120 3.2 Colleagues and a Friend 125 3.3 Teaching in Zurich 128 3.4 Scientific Work in Zurich 129 3.4.1 Game Theory 129 3.4.2 Algebra and Set Theory 133 3.4.3 Ordinal Numbers 133 3.5 The Fraenkel Correspondence of 1921 and the Axiom of Replacement 135 Freiburg 1921-1953 139 4.1 A New Start 139 4.2 Research in Applied Mathematics 148 4.2.1 The Calculation of Tournament Results 148 4.2.2 The Zermelo Navigation Problem 150 4.2.3 On Splitting Lines of Ovals 152 4.3 The Return to the Foundations of Mathematics ?. 153 4.3.1 The Return 153 4.3.2 The Logic Project , 154 4.3.3 Cantor's Collected Papers and the Relationship to Abraham Fraenkel 158 4.3.4 The Notgemeinschaft Project 163 4.4 Warsaw 1929 165 4.4.1 The Prehistory 165 4.4.2 The Warsaw Programme 167 4.4.3 The Nature of Mathematics 169 4.4.4 Intuitionism versus Mathematics of the Infinite 170 4.4.5 The Justification Problem 171 4.5 Foundational Controversies: An Introduction 175 4.6 Definiteness Revisited 179 4.6.1 Definiteness Until 1930 179 4.6.2 Incorporating Definiteness Into the Notion of Set 183 4.7 The Cumulative Hierarchy 186 4.7.1 Genesis 187 4.7.2 The Zermelo-Fraenkel Axiom System 189 4.7.3 Cumulative Hierarchies, Large Cardinals, and the Paradoxes 190 4.7.4 Continuation 193 4.7.5 The Reception of the Grenzzahlen Paper 194 4.8 The Skolem Controversy 196 4.8.1 The Lowenheim-Skolem Theorem 198 4.8.2 Skolem's Paradox 198 4.8.3 A "War" Against Skolem .4.9.2 Infinitary Languages 206 4.9.3 Infinitary Logic 208 4.9.4 Infinitary Languages and the Cumulative Hierarchy . . 209 4.9.5 The Failure 210 4.10 The Godel Controversy 212 4.10.1 The Bad Elster Conference 212 4.10.2 The Godel Correspondence 216 4.10.3 After the Controversy # 218 4.11 The Loss of the Honorary Professorship 219 4.11.1 The University of Freiburg and Its Mathematical Institute After the Seizure of Power 220 4.11.2 The Zermelo Case 224 4.11.3 After the Renunciation 231 4.12 Retreat 236 4.12.1 Giinterstal ; 237 4.12.2 Last Scientific Activities 4.12.3 The Time of Resignation 247 4.13 Twilight of Life 249 5 A Final Word 259 6 Zermelo's Curriculum Vitae 263 7 Appendix Selected Original Versions 273 7.1 Berlin 273 7.2 Gottingen 274 7.3 Zurich 282 7.4 Freiburg 287 References 307 Index ISBN 9783540495512