This paper introduces a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard—Vessiot theory recently developed by Matzat and van der Put. We use the methods and framework provided by the model theory of iterative differential fields. We offer a definition of strongly normal extension of iterative differential fields, and then prove that these extensions have good Galois theory and that a G-primitive element theorem holds. In addition, making (...) use of the basic theory of arc spaces of algebraic groups, we define iterative logarithmic equations, finally proving that our strongly normal extensions are Galois extensions for these equations. (shrink)

Jairo Moreno adapts the methodologies and nomenclature of Foucault’s "archaeology of knowledge" and applies it through individual case studies to the theoretical writings of Zarlino, Descartes, Rameau, and Weber. His conclusion summarizes the conditions—musical, philosophical, and historical—that "make a certain form of thought about music necessary and possible at the time it emerges." Musical Meaning and Interpretation—Robert S. Hatten, editor.