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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A property of arithmetic sets


Author: Hisao Tanaka
Journal: Proc. Amer. Math. Soc. 31 (1972), 521-524
DOI: https://doi.org/10.1090/S0002-9939-1972-0286661-1
MathSciNet review: 0286661
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Abstract | References | Additional Information

Abstract: We shall show that every nonempty countable arithmetic subset of $ {N^N}$ contains at least one element $ \alpha $ such that the singleton $ \{ \alpha \} $ itself is arithmetic. The proof is carried out by using a method in classical descriptive set theory.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0286661-1
Keywords: Arithmetic (i.e., $ \Pi _n^0$ or $ \Sigma _n^0$) subset of $ {N^N}$, arithmetic singleton, dense-in-itself, perfect set
Article copyright: © Copyright 1972 American Mathematical Society

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