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- A Presentation of Current Research on Partitions of Lines and Space
- We present the results from three papers concerning partitions of vector spaces V over the set R of reals and of the set of lines in V.
- The Computation of Ultrapowers by Supercompactness Measures
- The results from this dissertation are a computation of ultrapowers by supercompactness measures and concepts related to such measures. The second chapter gives an overview of the basic ideas required to carry out the computations. Included are preliminary ideas connected to measures, and the supercompactness measures. Order type results are also considered in this chapter. In chapter III we give an alternate characterization of 2 using the notion of iterated ordinal measures. Basic facts related to this characterization are also considered here. The remaining chapters are devoted to finding bounds fwith arguments taking place both inside and outside the ultrapowers. Conditions related to the upper bound are given in chapter VI.
- On the Cohomology of the Complement of a Toral Arrangement
- The author did not provide an abstract. The dissertation uses a number of mathematical formula including de Rham cohomology with complex coefficients to state and prove extension of Brieskorn's Lemma theorem.