Quantifier rank spectrum of L-infinity-omega

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Ackerman, Nathaniel Leedom

Advisor dc:contributor.advisor

• Gerald Sacks.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34269

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34269