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Tameness Results for Expansions of the Real Field by Groups
Tychonievich, Michael Andrew

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.

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Tychonievich, M. (2013). Tameness Results for Expansions of the Real Field by Groups . (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Tychonievich, Michael. "Tameness Results for Expansions of the Real Field by Groups ." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Tychonievich, Michael "Tameness Results for Expansions of the Real Field by Groups ." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

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