Notre Dame Journal of Formal Logic 52 (3):229-243 (2011)
| Abstract |
In this paper, we introduce a system of nonstandard second-order arithmetic $\mathsf{ns}$-$\mathsf{WWKL_0}$ which consists of $\mathsf{ns}$-$\mathsf{BASIC}$ plus Loeb measure property. Then we show that $\mathsf{ns}$-$\mathsf{WWKL_0}$ is a conservative extension of $\mathsf{WWKL_0}$ and we do Reverse Mathematics for this system
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| Keywords | second-order arithmetic nonstandard analysis reverse mathematics weak weak Koeonig's lemma Martin-Loef random |
| Categories | (categorize this paper) |
| Reprint years | 2011 |
| DOI | 10.1215/00294527-1435429 |
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References found in this work BETA
Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
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.
Relativizing Chaitin's Halting Probability.Rod Downey, Denis R. Hirschfeldt, Joseph S. Miller & André Nies - 2005 - Journal of Mathematical Logic 5 (02):167-192.
The Self-Embedding Theorem of WKL0 and a Non-Standard Method.Kazuyuki Tanaka - 1997 - Annals of Pure and Applied Logic 84 (1):41-49.
Citations of this work BETA
The Strength of Compactness in Computability Theory and Nonstandard Analysis.Dag Normann & Sam Sanders - 2019 - Annals of Pure and Applied Logic 170 (11):102710.
Reverse Mathematics and Parameter-Free Transfer.Benno van den Berg & Sam Sanders - 2019 - Annals of Pure and Applied Logic 170 (3):273-296.
Propagation of Partial Randomness.Kojiro Higuchi, W. M. Phillip Hudelson, Stephen G. Simpson & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):742-758.
Nonstandard Second-Order Arithmetic and Riemannʼs Mapping Theorem.Yoshihiro Horihata & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):520-551.
Cone Avoidance and Randomness Preservation.Stephen G. Simpson & Frank Stephan - 2015 - Annals of Pure and Applied Logic 166 (6):713-728.
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