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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Maximal $ \alpha $-r.e. sets


Author: Manuel Lerman
Journal: Trans. Amer. Math. Soc. 188 (1974), 341-386
MSC: Primary 02F27
DOI: https://doi.org/10.1090/S0002-9947-1974-0332458-X
MathSciNet review: 0332458
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Abstract: Various generalizations of maximal sets from ordinary recursion theory to recursion theory on admissible ordinals are considered. A justification is given for choosing one of these definitions as superior to the rest. For all the definitions considered to be reasonable, a necessary and sufficient condition for the existence of such maximal $ \alpha $-r.e. sets is obtained.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0332458-X
Keywords: Admissible ordinal, $ \alpha $-finite set, $ \alpha $-recursive set, $ \alpha $-r.e. set, maximal set, lattice of $ \alpha $-r.e. sets
Article copyright: © Copyright 1974 American Mathematical Society