Quantifier rank spectrum of L-infinity-omega
Author(s)Ackerman, Nathaniel Leedom
Massachusetts Institute of Technology. Dept. of Mathematics.
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In Part A we will study the quantifier rank spectrum of sentences of L!1,!. We will show that there are scattered sentences with models of arbitrarily high but bounded quantifier rank. We will also consider the case of weakly scattered and almost scattered sentences, and we will make some conjectures. In Part B we will look at a new method of induction in the case of sheaves. We will then use this method to generalize the classical proof of the Suslin-Kleene Separation Theorem to the context of sheaves on a partial Grothendieck topology.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 321) and index.
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology