A Nonstandard Counterpart of WWKL

Notre Dame Journal of Formal Logic 52 (3):229-243 (2011)
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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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Citations of this work

Reverse Mathematics and parameter-free Transfer.Benno van den Berg & Sam Sanders - 2019 - Annals of Pure and Applied Logic 170 (3):273-296.
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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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.
Almost everywhere domination and superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
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.

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