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Minkowski's Linear Forms Theorem in Elementary Function Arithmetic

Knapp, Greg
http://rave.ohiolink.edu/etdc/view?acc_num=case1495545998803274

Abstract Details

2017, Master of Sciences, Case Western Reserve University, Mathematics.
A classical question in formal logic is "how much mathematics do we need to know in order to prove a given theorem?" Of particular interest is Harvey Friedman's grand conjecture: that every known mathematical theorem involving only finitary mathematical objects can be proven from Elementary Function Arithmetic (EFA)—a fragment of Peano Arithmetic. If Friedman's conjecture is correct, this would imply that Fermat's Last Theorem is derivable from the axioms of EFA. The vast task of proving Fermat's Last Theorem from the axioms of EFA seems to require certain theorems on convex polytopes and an important corollary: Minkowski's Linear Forms Theorem. I show that certain theorems of convex geometry—e.g. representation of polytopes both in vertex form and as the intersection of half-spaces, monotonicity of volume, the existence of a separating plane between disjoint polytopes, and Minkowski's Linear Forms Theorem—can be both interpreted and derived in EFA, assuming the well-definedness of volume of a convex polytope along with one other technical lemma.
Colin McLarty (Advisor)
Mark Meckes (Committee Member)
David Singer (Committee Member)
Elisabeth Werner (Committee Member)
51 p.
Logic; Mathematics
minkowskis linear forms theorem; elementary function arithmetic; first-order arithmetic; convex geometry; polytope; volume; triangulation

Recommended Citations

Citations

  • Knapp, G. (2017). Minkowski's Linear Forms Theorem in Elementary Function Arithmetic [Master's thesis, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1495545998803274

    APA Style (7th edition)

  • Knapp, Greg. Minkowski's Linear Forms Theorem in Elementary Function Arithmetic. 2017. Case Western Reserve University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1495545998803274.

    MLA Style (8th edition)

  • Knapp, Greg. "Minkowski's Linear Forms Theorem in Elementary Function Arithmetic." Master's thesis, Case Western Reserve University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1495545998803274

    Chicago Manual of Style (17th edition)

case1495545998803274
692
© 2017, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.