Cardinals as ultrapowers [Elektronische Ressource] : a canonical measure analysis under the axiom of determinacy / vorgelegt von Stefan Bold

Cardinals as UltrapowersA Canonical Measure Analysisunder the Axiom of DeterminacyDissertationzurErlangung des Doktorgrades (Dr. rer. nat.)derMathematisch-Naturwissenschaftlichen Fakult¨ atderRheinischen Friedrich-Wilhelms-Universitat¨ Bonnvorgelegt vonStefan BoldausMainz-MombachBonn 2009Angefertigt mit Genehmigung der Mathematisch-NaturwissenschaftlichenFakult¨ at der Rheinischen Friedrich-Wilhelms-Universit¨ at Bonn.Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonn unterhttp://hss.ulb.uni-bonn.de/diss online elektronisch publiziert.Erscheinungsjahr 20091. Gutachter: Prof. Dr. Benedikt L¨ owe2.hter: Prof. Dr. Peter KoepkeTag der Promotion: 5. November 2009PrefaceThe game is up.William Shakespeare (1564 - 1616)“Cymbeline”, Act 3 scene 3My interest in logic and set theory was first raised when I realized that math-ematics is not just about calculations with numbers but about formal systems,about the consequences that follow from applying specific rules to formal state-ments, so that the whole of mathematics can be concluded from axioms and rulesof deduction. After reading about G¨ odels theorems I was fascinated. This waswhen I was still in high school and my first years of studying mathematics weremore concerned with topics like functional analysis and algebraic topology.Then I had to decide what the topic of my Master’s thesis should be. I re-membered that I always wanted to know more about set theory.