Thinning Operators and Pi 4 -Reflection

Erweitert man das Axiomensystem der Kripke-Platek-Mengenlehre um ein Reflexionsschema für \Pi_4-Formeln, so erhält man das System der \Pi_4-Reflexion. Einen anschaulichen beweistheoretischen Zugang zu diesem bietet die Technik der Ausdünnhierarchien. Diese basiert auf der transfiniten Iteration von Ausdünnoperatoren, welche durch Verkleinern von Klassen von Modellkandidaten gewährleisten, daß im Kollabierungsverfahren Reflexionsregeln eliminiert werden können. Durch Untersuchung von speziellen Herleitungen läßt sich mit diesem Ansatz eine Ordinalzahlanalyse durchführen

Herkules – Held zwischen Tugend und Hybris. Ein europäischer Erinnerungsort der Frühen Neuzeit?

This essay traces some of the contexts and media in which "Heracles-Hercules" - as a hero between virtue and hubris - was visible in European societies from the end of the middle ages onwards. It discusses whether this example of the reception, appropriation and transformation of classical myths in the early modern period can be understood as a European "lieu de mémoire", and to what extent the concept of "lieux de mémoire" (or sites of memory) can foster our understanding of a particular object of study (here the Heracles/Hercules myth). Against this backdrop, we conclude with some general questions about the more ambitious project* of a comprehensive register of European "lieux de mémoire". * * Published as: Boer, Pim den / Duchhardt, Heinz / Kreis, Georg / Schmale, Wolfgang (eds.): Europäische Erinnerungsorte, 3 vols., Munich 2011–201

Exploring the reliability, validity, and dimensionality of the 'Kieler kindergarten test for mathematics' [Een exploratief onderzoek naar de betrouwbaarheid, validiteit en dimensionaliteit van de 'Kieler kindergarten test for mathematics']

Mathematical literacy consists of several content areas. However, in kindergarten, most assessments focus solely on the number area. It is yet unknown whether the content areas of mathematical literacy can already be distinguished in young children. The Kieler Kindergartentest for Mathematics (KiKi) is a German instrument that is developed to measure performance in five content areas of mathematics in kindergarten (4;0 – 6;6 years of age). The KiKi was translated into Dutch and administered in 244 children. IRT analyses were adopted to examine reliability and validity evidence for the instrument and to examine the dimensionality of mathematics in Dutch kindergarten. The reliability as well as convergent and discriminant validity evidence were generally good. A three-dimensional model with the dimensions number (including measurement and change and relationships), space and shape, and data and chance showed the best fit. This indicates that some but not all content areas can be distinguished in kindergarten. Implications for theory and educational practice are discussed