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Authors:	Sy D Friedman

Institution:	Department of Mathematics Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Abstract:	We use ``iterated square sequences' to show that there is an -definable partition $n:L{\text-}Singulars \to \omega$ such that if is an inner model not containing $0^\#$ : (a) For some $k, M \models \{\alpha\|n(\alpha)\leq k\}$ is stationary. (b) For each there is a generic extension of in which $0^\#$ does not exist and $\{\alpha\|n(\alpha)\leq k\}$ is non-stationary. This result is then applied to show that if is an inner model without $0^\#$ , then some $\Sigma^1_3$ sentence not true in can be forced over .

Keywords:	Class forcing absoluteness partitions

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