TY - JOUR
T1 - A compactness theorem for singular cardinals, free algebras, Whitehead problem and tranversals
AU - Shelah, Saharon
PY - 1975/12
Y1 - 1975/12
N2 - 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 on S k(A). As an application we conclude that V=L implies that every Whitehead group is free.
AB - 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 on S k(A). As an application we conclude that V=L implies that every Whitehead group is free.
UR - http://www.scopus.com/inward/record.url?scp=51649173218&partnerID=8YFLogxK
U2 - 10.1007/BF02757993
DO - 10.1007/BF02757993
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AN - SCOPUS:51649173218
SN - 0021-2172
VL - 21
SP - 319
EP - 349
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 4
ER -