### Not collapsing cardinals $\leq\kappa$ in $(<\kappa)$--support iterations

by Shelah. [Sh:587]

Israel J Math, 2003

We deal with the problem of preserving various versions of
completeness in (< kappa) --support iterations of forcing notions,
generalizing the case ``S --complete proper is preserved by CS
iterations for a stationary co-stationary S subseteq omega_1''. We
give applications to Uniformization and the Whitehead problem. In
particular, for a strongly inaccessible cardinal kappa and a
stationary set S subseteq kappa with fat complement we can have
uniformization for < A_delta : delta in S'>, A_delta
subseteq delta = sup A_delta, cf(delta)=otp(A_delta) and a
stationary non-reflecting set S' subseteq S .

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