2026-09-20T01:54:28Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/342692022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Gerald Sacks.
Ackerman, Nathaniel Leedom
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-10-31T15:21:09Z
2006-10-31T15:21:09Z
2006
2006
http://hdl.handle.net/1721.1/34269
71015686
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.
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.
by Nathaniel Leedom Ackerman.
Ph.D.
321 p.
1495538 bytes
1490131 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Quantifier rank spectrum of L-infinity-omega
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="8fad26f0-2920-42cf-8c87-878e13f8dc3e">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Quantifier rank spectrum of L-infinity-omega</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2006</PublicationDate>
<Authors>
<Author>
<DisplayName>Ackerman, Nathaniel Leedom</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<Abstract>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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>