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Journal of the London Mathematical Society 1980 s2-21(1):1-12; doi:10.1112/jlms/s2-21.1.1
© 1980 by London Mathematical Society
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© Oxford University Press

A Hall Criterion for Countable Families of Sets

Michael Holz, Klaus-Peter Podewski and Karsten Steffens

Institut für Mathematik, Universität Hannover 3000 Hannover, W. Germany

Let F = (F(i)|i {varepsilon} I) be a countable family. By recursion we define subsets I{alpha}(B) of I and prove that there is an ordinal {lambda} such that F has an injective choice function if and only if |B| ≥ |{cup}{I{gamma}(B)|{gamma} < {lambda}) | for every finite set B.


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