On the divergence of extension procedures in isol theory

McLaughlin, T. G.

doi:10.1090/S0002-9939-1981-0630052-3

On the divergence of extension procedures in isol theory
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by T. G. McLaughlin PDF

Proc. Amer. Math. Soc. 83 (1981), 769-773 Request permission

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.

References

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