Representations of Reals in Reverse Mathematics

Jeffry L. Hirst¹

¹ Department of Mathematical Sciences Appalachian State University Boone, NC 28608, U.S.A.

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 303-316.

Résumé

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 ${\mathsf{R}\mathsf{C}\mathsf{A}}_0$. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of ${\mathsf{W}\mathsf{K}\mathsf{L}}_0$ or ${\mathsf{A}\mathsf{C}\mathsf{A}}_0$.

Détail

DOI : 10.4064/ba55-4-2

Mots-clés : working framework reverse mathematics consider representations reals rapidly converging cauchy sequences decimal expansions sorts dedekind cuts converting single reals representation another always carried out rca however conversion process always uniform converting infinite sequences reals representations other representations requires wkl aca