Representations of Reals in Reverse Mathematics

Volume 55 / 2007

Jeffry L. Hirst Bulletin Polish Acad. Sci. Math. 55 (2007), 303-316 MSC: 03B30, 03F35, 03F60. DOI: 10.4064/ba55-4-2

Abstract

Working in the framework of reverse mathematics, we consider representations of reals as rapidly converging Cauchy sequences, decimal expansions, and two sorts of Dedekind cuts. Converting single reals from one representation to another can always be carried out in ${\sf{RCA}}_0$. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of ${\sf{WKL}}_0$ or ${\sf{ACA}}_0$.

Authors

  • Jeffry L. HirstDepartment of Mathematical Sciences
    Appalachian State University
    Boone, NC 28608, U.S.A.
    e-mail

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