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On a Π01 Set of Positive Measure

Published online by Cambridge University Press:  22 January 2016

Hisao Tanaka
Hisao Tanaka*
Affiliation:
Hosei University
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Some basis results for arithmetic, hyperarithmetic (HA) or sets which have positive measure (or which are not meager, i.e., of the second Baire category) have been obtained by several authors. For example, every non-meager set must have a recursive element (Shoenfield-Hinman, Hinman [2]) but there exists a non-meager set (as well as of measure 1) that contains no recursive element (Shoenfield [7]), and every set (i.e., arithmetic set) of positive measure contains an arithmetic element (Sacks [5], and Tanaka [12]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 139 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

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