Annals of the Japan Association for Philosophy of Science
Online ISSN : 1884-1228
Print ISSN : 0453-0691
ISSN-L : 0453-0691
Special Section: Computability Theory and the Foundation of Mathematics
Rudin's Lemma and Reverse Mathematics
Gaolin LIJunren RUGuohua WU
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2017 Volume 25 Pages 57-66

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Abstract

Domain theory formalizes the intuitive ideas of approximation and convergence in a very general way, and provides a fundamental tool in the study of computing theory and computability theory. In search of complete lattices on which the Laswon topology is Hausdorff, Gierz, Lawson and Stralka introduced in [3] quasicontinuous lattices, which inherit many good properties of domains. Gierz, et al. pointed in [3] that Rudin's Lemma for finding a “cross-section” of certain descending family of sets plays a central role in the development of the whole theory of quasicontinuous lattices. In this paper, we study Rudin's Lemma from reverse mathematics point of view and prove that the Rudin's Lemma is equivalent to ACA0 over RCA0.

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© 2017 Annals of the Japan Association for Philosophy of Science
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