The Borel Complexity of Isomorphism for Some First Order Theories

In this work we consider several instances of the following problem: "how complicated can the isomorphism relation for countable models be?"' Using the Borel reducibility framework, we investigate this question with regard to the space of countable models of particular complete first-order theories. We also investigate to what extent this complexity is mirrored in the number of back-and-forth inequivalent models of the theory. We consider this question for two large and related classes of theories. First, we consider o-minimal theories, showing that if T is o-minimal, then the isomorphism relation is either Borel complete or Borel. Further, if it is Borel, we characterize exactly which values can occur, and when they occur. In all cases Borel completeness implies lambda-Borel completeness for all lambda. Second, we consider colored linear orders, which are (complete theories of) a linear order expanded by countably many unary predicates. We discover the same characterization as with o-minimal theories, taking the same values, with the exception that all finite values are possible except two. We characterize exactly when each possibility occurs, which is similar to the o-minimal case. Additionally, we extend Schirrman's theorem, showing that if the language is finite, then T is countably categorical or Borel complete. As before, in all cases Borel completeness implies lambda-Borel completeness for all lambda.

The Many Faces of Paul Hindemith

The purpose of this project is to present selected violin pieces by Paul Hindemith (1895-1963) against a backdrop of the diverse styles and traditions that he integrated in his music. For this dissertation project, selected violin sonatas by Hindemith were performed in three recitals alongside pieces by other German and Austro-German composers. These recitals were also recorded for archival purposes. The first recital, performed with pianist David Ballena on December 10, 2005, in Gildenhorn Recital Hall at the University of Maryland, College Park, included Violin Sonata Op.11, No. 1 (1918) by Paul Hindemith, Sonatina in D Major, Op. 137 (1816) by Franz Schubert, and Sonata in E-flat Major, Op.18 (1887) by Richard Strauss. The second recital, performed with pianist David Ballena on May 9, 2006, in Gildenhorn Recital Hall at the University of Maryland, included Sonata in E Minor, KV 304 (1778) by Wolfgang Amadeus Mozart, Sonata in E (1935) by Paul Hindemith, Romance for Violin and Orchestra No.1 in G Major (1800-1802) by Ludwig Van Beethoven, and Sonata for Violin and Piano in A minor, Op. 105 (1851) by Robert Schumann. The third recital, performed with David Ballena and Kai-Ching Chang on November 10, 2006 in Ulrich Recital Hall at the University of Maryland, included Violin Sonata Op.12 No.1 in D Major (1798) by Ludwig Van Beethoven, Sonata for Violin and Harpsichord No.4 in C Minor BWV 1017 (1720) by J.S. Bach, and Violin Sonata Op.11 No.2 (1918) by Paul Hindemith. For each of my dissertation recitals, I picked a piece by Hindemith as the core of the program then picked pieces by other composers that have similar key, similar texture, same number of movements or similar feeling to complete my program. Although his pieces used some classical methods of composition, he added his own distinct style: extension of chromaticism; his prominent use of interval of the fourth; his chromatic alteration of diatonic scale degrees; and his non-traditional cadences. Hindemith left behind a legacy of multi-dimensional, and innovative music capable of expressing both the old and the new aesthetics.