Notre Dame Journal of Formal Logic

A Nonstandard Counterpart of WWKL

Stephen G. Simpson and Keita Yokoyama


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.

Article information

Notre Dame J. Formal Logic Volume 52, Number 3 (2011), 229-243.

First available in Project Euclid: 28 July 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F35: Second- and higher-order arithmetic and fragments [See also 03B30]
Secondary: 26E35: Nonstandard analysis [See also 03H05, 28E05, 54J05]

second-order arithmetic nonstandard analysis reverse mathematics weak weak Koeonig's lemma Martin-Loef random


Simpson, Stephen G.; Yokoyama, Keita. A Nonstandard Counterpart of WWKL. Notre Dame J. Formal Logic 52 (2011), no. 3, 229--243. doi:10.1215/00294527-1435429.

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