Representations of Reals in Reverse Mathematics
Volume 55 / 2007
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 ${\sf{ACA}}_0$.
