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On the effectiveness of the Schröder-Bernstein theorem

Author: J. B. Remmel
Journal: Proc. Amer. Math. Soc. 83 (1981), 379-386
MSC: Primary 03D20
MathSciNet review: 624936
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Abstract: The effectiveness of the classical equivalence theorem of Schröder and Bernstein is investigated using the tools of recursion theory. We prove one result which generalizes all the effective versions of the Schröder-Bernstein theorem which occur in the literature. In contrast, we show that Banach's strengthening of the Schröder-Bernstein theorem fails to be effective.

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