|
Set Theory and the Continuum Hypothesis SemesterWiSe 2018 / 19 Lecturer Holger Leuz, Clara Löh Type of course (Veranstaltungsart) Seminar Contents The classical foundation of Mathematics consists of Logic and Set Theory. A popular formalisation of Set Theory is through the Zermelo-Fraenkel axioms (and the Axiom of Choice). An innocent-looking assumption about basic set theory is that there is no set whose cardinality is strictly between the cardinality of the natural numbers and the real numbers (Continuum Hypothesis). In the early days of Set Theory, it was one of the fundamental open problems to determine whether the Continuum Hypothesis holds or not -- in fact, this is the first of the list of Hilbert's problems from 1900. Surprisingly, it turns out that the Continuum Hypothesis is independent from ZFC, i.e., that one can neither prove nor disprove the Continuum Hypothesis from ZFC (!). Gödel proved in 1940 that CH cannot be disproved from ZFC; Cohen established in 1963 that CH also cannot be proved from ZFC (thus winning the Fields Medal in 1966). In this seminar, we will develop the basics of Set Theory needed to properly formalise and prove these results. This result is also important for the epistemology of mathematics as it shows us certain limits for the classical foundation of mathematics and for the for axiomatic method in general. Recommended previous knowledge none (except some maturity with formal reasoning) Time/Date Mo 12:30--14:00 Location M 103 Course homepage http://www.mathematik.uni-r.de/loeh/teaching/setsem_ws1819/ (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
This seminar is jointly organised with Dr. Holger Leuz (Institut für Philosophie) Modules BSem, MV, MSem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 |