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Proceedings of the American Mathematical Society

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

 

 

Rich sets


Author: C. T. Chong
Journal: Proc. Amer. Math. Soc. 80 (1980), 458-460
MSC: Primary 03D60; Secondary 03D30
MathSciNet review: 581005
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Abstract: Let $ {(V = L)_\alpha }$ say that every bounded subset of $ \alpha $ is an element of $ {L_\alpha }$. We show that if $ {(V = L)_\alpha }$, then every $ X \subseteq \alpha $ of order-type $ \alpha $ is rich, in the sense that every $ \alpha $-degree above that of X is represented by a subset of X.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0581005-4
Keywords: Rich sets, $ \alpha $-recursive, $ \alpha $-degree, $ \alpha $-finite, homogeneous
Article copyright: © Copyright 1980 American Mathematical Society