Papers
・
The Jordan curve theorem and the Schönflies
theorem in weak second-order arithmetic, (with
Archive for Mathematical Logic 46, pages: 465-480, July 2007.
・ Non-standard analysis in ACA0 and Riemann mapping theorem,
Mathematical Logic Quarterly 53, Issue 2, Pages: 132-146, April 2007.
・ Complex analysis in subsystems of second order arithmetic,
Archive for Mathematical Logic 46, pages: 15-35, January 2007.
・ Reverse Mathematics for Fourier expansion,
in; Arnold Beckmann, Costas Dimitracopoulos, and Benedikt Löwe (eds.): Logic and Theory of Algorithms, Fourth Conference on Computability in Europe, CiE 2008, Athens, Greece, June 2008, Local Proceedings, pages: 473-482.
・ Singularities of Holomorphic Functions in Subsystems of Second Order Arithmetic, (with Y. Horihata)
in; Arnold Beckmann, Costas Dimitracopoulos, and Benedikt Löwe (eds.): Logic and Theory of Algorithms, Fourth Conference on Computability in Europe, CiE 2008, Athens, Greece, June 2008, Local Proceedings, pages: 157-164.
・ Formalizing non-standard arguments in second-order arithmetic, to appear.
・ On Pi11 conservativity for Pi12 theories in second order arithmetic,
in;Chong Chi Tat, Rod Downey, Joerg Brendle, Qi Feng, Hirotaka Kikyo, Hiroakira Ono and Toshiyasu Arai (eds.): Proceedings of the 10th Asian Logic Conference, World Scientific, November 2009, pages: 375-386.
・ Standard and non-standard analysis in second order arithmetic, Tohoku Mathematical Publications No. 34, June 2009.
・ A non-standard counterpart of WWKL, (with S. Simpson), preprint.
・ Reverse Mathematics for Non-standard analysis, preprint.