Computability in Europe 2008
Logic and Theory of Algorithms

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Regular Talk:
Singularities of Holomorphic Functions in Subsystems of Second Order Arithmetic

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Author(s): Yoshihiro Horihata and Keita Yokoyama
Slot: Tue, 11:20-11:40, Amphitheater A (col. 1)

Abstract

We study complex analysis in the context of weak subsystems of second order
arithmetic.
We are mainly concerned with integrability and singularities of holomorphic
functions.
Then, we develop a part of complex analysis concerned with Picard's little
theorem.
We show that Picard's little theorem is provable from WKL_0 plus a version
of the Riemann mapping theorem.
Since a full version of the Riemann mapping theorem is provable in ACA_0, we can
prove Picard's little theorem in ACA_0.

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