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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 systemOther Versions
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Citations of this work
Computability theory, nonstandard analysis, and their connections.Dag Normann & Sam Sanders - 2019 - Journal of Symbolic Logic 84 (4):1422-1465.
The reverse mathematics of theorems of Jordan and lebesgue.André Nies, Marcus A. Triplett & Keita Yokoyama - 2021 - Journal of Symbolic Logic 86 (4):1657-1675.
From Display to Labelled Proofs for Tense Logics.Agata Ciabattoni, Tim Lyon & Revantha Ramanayake - 2013 - In Sergei Artemov & Anil Nerode, Logical Foundations of Computer Science (Lecture Notes in Computer Science 7734). Springer. pp. 120 - 139.
The strength of compactness in Computability Theory and Nonstandard Analysis.Dag Normann & Sam Sanders - 2019 - Annals of Pure and Applied Logic 170 (11):102710.
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.
References found in this work
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
Relativizing chaitin's halting probability.Rod Downey, Denis R. Hirschfeldt, Joseph S. Miller & André Nies - 2005 - Journal of Mathematical Logic 5 (2):167-192.
Almost everywhere domination and superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Some conservation results on weak König's lemma.Stephen G. Simpson, Kazuyuki Tanaka & Takeshi Yamazaki - 2002 - Annals of Pure and Applied Logic 118 (1-2):87-114.
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