Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
Perron, Michael Accepted Dissertation 3-14-17 Sp17.pdf (422.29 KB)
ETD Abstract Container
Abstract Header
On the Structure of Independent Families
Author Info
Perron, Michael J.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490003394000281
Abstract Details
Year and Degree
2017, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
Abstract
A paper by Shelah that established the consistency of i < u gave an independent family with a host of properties. This dissertation investigates how these properties give rise to different varieties of independent families. We explore the connection between independent families and ultrafilters. We us Martins Axiom as a guide for looking at the generic existence of independent families. We show that selective independent families are preserved in both Iterated Sacks Forcing and Side-by-side Sacks Forcing.
Committee
Todd Eisworth (Advisor)
Vladimir Uspenskiy (Committee Member)
Sergio Lopez (Committee Member)
Philip Ehrlich (Committee Member)
Pages
69 p.
Subject Headings
Mathematics
Keywords
independent families
;
independence number
;
selective
;
Sacks forcing
;
diamond
;
generic existence
;
Martins Axiom
;
dense independent
;
q-independent
;
p-independent
;
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Perron, M. J. (2017).
On the Structure of Independent Families
[Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490003394000281
APA Style (7th edition)
Perron, Michael.
On the Structure of Independent Families.
2017. Ohio University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490003394000281.
MLA Style (8th edition)
Perron, Michael. "On the Structure of Independent Families." Doctoral dissertation, Ohio University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490003394000281
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
ohiou1490003394000281
Download Count:
1,097
Copyright Info
© 2017, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.