Nonstandard second-order arithmetic and Riemannʼs mapping theorem
Annals of Pure and Applied Logic 165 (2):520-551 (2014)
Abstract
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 Riemannʼs mapping theorem, and show several different versions of Riemannʼs mapping theoremDOI
10.1016/j.apal.2013.06.022
My notes
Similar books and articles
Non-standard analysis in ACA0 and Riemann mapping theorem.Keita Yokoyama - 2007 - Mathematical Logic Quarterly 53 (2):132-146.
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Tennenbaum's Theorem and Unary Functions.Sakae Yaegasi - 2008 - Notre Dame Journal of Formal Logic 49 (2):177-183.
The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic.Nobuyuki Sakamoto & Keita Yokoyama - 2007 - Archive for Mathematical Logic 46 (5-6):465-480.
The strength of nonstandard methods in arithmetic.C. Ward Henson, Matt Kaufmann & H. Jerome Keisler - 1984 - Journal of Symbolic Logic 49 (4):1039-1058.
Complex analysis in subsystems of second order arithmetic.Keita Yokoyama - 2007 - Archive for Mathematical Logic 46 (1):15-35.
Transfer principles in nonstandard intuitionistic arithmetic.Jeremy Avigad & Jeffrey Helzner - 2002 - Archive for Mathematical Logic 41 (6):581-602.
Nonstandard Models and Kripke's Proof of the Gödel Theorem.Hilary Putnam - 2000 - Notre Dame Journal of Formal Logic 41 (1):53-58.
Hindman's theorem: An ultrafilter argument in second order arithmetic.Henry Towsner - 2011 - Journal of Symbolic Logic 76 (1):353 - 360.
Regularity in models of arithmetic.George Mills & Jeff Paris - 1984 - Journal of Symbolic Logic 49 (1):272-280.
Separations of first and second order theories in bounded arithmetic.Masahiro Yasumoto - 2005 - Archive for Mathematical Logic 44 (6):685-688.
An Effective Conservation Result for Nonstandard Arithmetic.Erik Palmgren - 2000 - Mathematical Logic Quarterly 46 (1):17-24.
Analytics
Added to PP
2014-01-16
Downloads
26 (#448,666)
6 months
1 (#447,993)
2014-01-16
Downloads
26 (#448,666)
6 months
1 (#447,993)
Historical graph of downloads
Citations of this work
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Tanaka’s theorem revisited.Saeideh Bahrami - 2020 - Archive for Mathematical Logic 59 (7-8):865-877.
References found in this work
Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
The self-embedding theorem of WKL0 and a non-standard method.Kazuyuki Tanaka - 1997 - Annals of Pure and Applied Logic 84 (1):41-49.