Geodesic
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ${\sf{ACA}}_0$.
DOI : 10.4064/ba55-4-2
Keywords: 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

Jeffry L. Hirst 1

1 Department of Mathematical Sciences Appalachian State University Boone, NC 28608, U.S.A. 
@article{10_4064_ba55_4_2,
     author = {Jeffry L. Hirst},
     title = {Representations of {Reals} in {Reverse} {Mathematics}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {303--316},
     publisher = {mathdoc},
     volume = {55},
     number = {4},
     year = {2007},
     doi = {10.4064/ba55-4-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba55-4-2/}
}
TY  - JOUR
AU  - Jeffry L. Hirst
TI  - Representations of Reals in Reverse Mathematics
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2007
SP  - 303
EP  - 316
VL  - 55
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba55-4-2/
DO  - 10.4064/ba55-4-2
LA  - en
ID  - 10_4064_ba55_4_2
ER  - 
%0 Journal Article
%A Jeffry L. Hirst
%T Representations of Reals in Reverse Mathematics
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2007
%P 303-316
%V 55
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ba55-4-2/
%R 10.4064/ba55-4-2
%G en
%F 10_4064_ba55_4_2
Jeffry L. Hirst. Representations of Reals in Reverse Mathematics. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 303-316. doi: 10.4064/ba55-4-2

Cité par Sources :