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Proceedings of the American Mathematical Society

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

 
 

 

On the divergence of extension procedures in isol theory


Author: T. G. McLaughlin
Journal: Proc. Amer. Math. Soc. 83 (1981), 769-773
MSC: Primary 03D50
DOI: https://doi.org/10.1090/S0002-9939-1981-0630052-3
MathSciNet review: 630052
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Abstract: We show that the Myhill and Nerode extensions begin to disagree on the domain of the Nerode extension at a point in the arithmetical hierarchy $ \leqslant \Delta _3^0$. This disagreement, at level $ \Delta _3^0$, goes hand in hand with a certain way in which the Myhill extension fails, at $ \Delta _3^0$, to commute with composition.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0630052-3
Article copyright: © Copyright 1981 American Mathematical Society

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