Ein Henkin-Vollständigkeitsbeweis für die intuitionistische Prädikatelogik bezüglich der Kripke-Semantik

Ohne Zusammenfassung     

Skolem-Normalformen

For simple type theory with -conversion, extensionality and classical, intuitionistic or minimal predicate logic together with M-, Br-, S4- or S5-modalities as examples it is shown that it is possible to obtain Skolemnormalforms only by applying transpositions, i.e. replacements of equivalent subformulae. In this way one gets in classical type theory without modalities a provable equivalent normalform with prefix and with S5-modalities a deductive equivalent prenex normalform of the form. The axiom of choice allows further simplifications: for example in classical simple type theory a provable equivalent normalform with prefix.     

Über das Markov-Prinzip

Ohne ZusammenfassungIn einer Fortsetzung dieser (im Mai 1974 abgeschlossenen) Arbeit wird die Untersuchung unter Berücksichtigung der inzwischen erschienenen Literatur weitergeführt.     

Aussagenlogisch Fundierte Theorien

Ohne ZusammenfassungDies ist der erste Teil einer Arbeit, die von der Naturwissenschaftlichen Fakultät der Phillips-Universität Marburg/Lahn als Dissertation angenommen wurde.Der Verfasser dankt seinem verehrten Lehrer, Herrn Professor H. Arnold Schmidt, der ihm in seinen Vorlesungen, seinen Seminaren und zahlreichen Gesprächen einen tiefen Kontakt zur Mathematik, insbesondere zur mathematischen Grundlagenforschung, vermittelt hat.     

A volume comparison theorem for characteristic numbers

We show that assuming lower bounds on the Ricci curvature and the injectivity radius the absolute value of certain characteristic numbers of a Riemannian manifold, including all Pontryagin and Chern numbers, is bounded proportionally to the volume. The proof relies on Chern–Weil theory applied to a connection constructed from Euclidean connections on charts in which the metric tensor is harmonic and has bounded Hölder norm. We generalize this theorem to a Gromov–Hausdorff closed class of rough Riemannian manifolds defined in terms of Hölder regularity. Assuming an additional upper Ricci curvature bound, we show that also the Euler characteristic is bounded proportionally to the volume. Additionally, we remark on a volume comparison theorem for Betti numbers of manifolds with an additional upper bound on sectional curvature. It is a consequence of a result by Bowen.

     

Experimental evidence of intermittent convection in the edge of magnetic confinement devices

Probe measurements in the PISCES linear device indicate the presence of plasma radially far from where it is produced. We show that this is mainly caused by large-scale structures of plasma with high radial velocity. Data from the Tore Supra tokamak show striking similarities in the shape of these intermittent events as well as the fluctuation density probability distribution and frequency spectrum. The fact that intermittent, large-scale events are so similar in linear devices and tokamaks indicates the universality of convective transport in magnetically confined plasmas.     

Kodifikation und Aussagenlogik

Ohne Zusammenfassung