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Tameness Results for Expansions of the Real Field by Groups

Tychonievich, Michael Andrew
http://rave.ohiolink.edu/etdc/view?acc_num=osu1367572291

Abstract Details

2013, Doctor of Philosophy, Ohio State University, Mathematics.
Expanding on the ideas of o-minimality, we study three kinds of expansions of the real field and discuss certain tameness properties that they possess or lack. We prove that the ring of integers is definable in the expansion of the real field by an infinite convex subset of a finite-rank additive subgroup of the reals. We give structure theorem for expansions of the real field by families of restricted complex power functions and apply it to classify expansions of the real field by families of locally closed trajectories of linear vector fields. We examine certain polynomially bounded o-minimal structures over the real field expanded by multiplicative subgroups of the reals. The main result is that any nonempty, bounded, definable d-dimensional submanifold has finite d-dimensional Hausdorff measure if and only if the dimension of its frontier is less than d.
Chris Miller (Advisor)
Timothy Carlson (Committee Member)
Ovidiu Costin (Committee Member)
55 p.
Logic; Mathematics
o-minimal; tameness; analytic geometry; definable

Recommended Citations

Citations

  • Tychonievich, M. A. (2013). Tameness Results for Expansions of the Real Field by Groups [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1367572291

    APA Style (7th edition)

  • Tychonievich, Michael. Tameness Results for Expansions of the Real Field by Groups . 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1367572291.

    MLA Style (8th edition)

  • Tychonievich, Michael. "Tameness Results for Expansions of the Real Field by Groups ." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1367572291

    Chicago Manual of Style (17th edition)

osu1367572291
746
© 2013, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.