Abstract
We prove, in an axiomatic way, a compactness theorem for singular cardinals. We apply it to prove that, for singular λ, every λ-free algebra is free; and similar compactness results for transversals and colouring numbers. For the general result on free algebras, we develop some filters onS k(A). As an application we conclude thatV=L implies that every Whitehead group is free.
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The author would like to acknowledge N.S.F. Grant 43901, by which he was partially supported, and to thank P. Eklof and A. Mekler for stimulating discussions.
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Shelah, S. A compactness theorem for singular cardinals, free algebras, Whitehead problem and tranversals. Israel J. Math. 21, 319–349 (1975). https://doi.org/10.1007/BF02757993
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DOI: https://doi.org/10.1007/BF02757993