A Nonstandard Counterpart of WWKL
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 systemDOI
10.1215/00294527-1435429
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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.
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.
