Representations of Reals in Reverse Mathematics

Jeffry L. Hirst. "Representations of Reals in Reverse Mathematics." Bulletin of the Polish Academy of Sciences. Mathematics 55.4 (2007): 303-316. <http://eudml.org/doc/281227>.

@article{JeffryL2007,
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 RCA₀. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of WKL₀ or ACA₀.},
author = {Jeffry L. Hirst},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {real analysis; Cauchy sequence; Dedekind cut; decimal expansion; reverse mathematics; WKL; ACA},
language = {eng},
number = {4},
pages = {303-316},
title = {Representations of Reals in Reverse Mathematics},
url = {http://eudml.org/doc/281227},
volume = {55},
year = {2007},
}

TY - JOUR
AU - Jeffry L. Hirst
TI - Representations of Reals in Reverse Mathematics
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
VL - 55
IS - 4
SP - 303
EP - 316
AB - 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 RCA₀. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of WKL₀ or ACA₀.
LA - eng
KW - real analysis; Cauchy sequence; Dedekind cut; decimal expansion; reverse mathematics; WKL; ACA
UR - http://eudml.org/doc/281227
ER -