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Proceedings of the American Mathematical Society

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

 
 

 

Index sets and Boolean operations


Author: Douglas E. Miller
Journal: Proc. Amer. Math. Soc. 84 (1982), 568-572
MSC: Primary 03D25; Secondary 03D55
DOI: https://doi.org/10.1090/S0002-9939-1982-0643751-5
MathSciNet review: 643751
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Abstract: Hay's thesis asserts that every naturally defined class of sets of natural numbers contains an index set which is $ 1$-complete for that class and that every index set is $ 1$-complete for some naturally defined class. We formalize "naturally defined" as "effective Boolean" and establish the thesis as a Metatheorem.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0643751-5
Keywords: Index sets, many-one degrees, hierarchies, Boolean set operations
Article copyright: © Copyright 1982 American Mathematical Society

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