TY - JOUR
T1 - Nonstandard second-order arithmetic and Riemann's mapping theorem
AU - Horihata, Yoshihiro
AU - Yokoyama, Keita
PY - 2014/2
Y1 - 2014/2
N2 - In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemann's mapping theorem, and show several different versions of Riemann's mapping theorem.
AB - In this paper, we introduce systems of nonstandard second-order arithmetic which are conservative extensions of systems of second-order arithmetic. Within these systems, we do reverse mathematics for nonstandard analysis, and we can import techniques of nonstandard analysis into analysis in weak systems of second-order arithmetic. Then, we apply nonstandard techniques to a version of Riemann's mapping theorem, and show several different versions of Riemann's mapping theorem.
KW - Nonstandard analysis
KW - Reverse mathematics
KW - Riemann's mapping theorem
KW - Second-order arithmetic
UR - http://www.scopus.com/inward/record.url?scp=84887993249&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84887993249&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2013.06.022
DO - 10.1016/j.apal.2013.06.022
M3 - Article
AN - SCOPUS:84887993249
SN - 0168-0072
VL - 165
SP - 520
EP - 551
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 2
ER -