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On the Structure of Independent Families

Perron, Michael J.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490003394000281

Abstract Details

2017, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
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.
Todd Eisworth (Advisor)
Vladimir Uspenskiy (Committee Member)
Sergio Lopez (Committee Member)
Philip Ehrlich (Committee Member)
69 p.
Mathematics
independent families; independence number; selective; Sacks forcing; diamond; generic existence; Martins Axiom; dense independent; q-independent; p-independent;

Recommended Citations

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)

ohiou1490003394000281
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This open access ETD is published by Ohio University and OhioLINK.