New Σ¹₃ facts
Sy D. Friedman · Proceedings of the American Mathematical Society · 1999
We use “iterated square sequences” to show that there is an L L - definable partition n : L - S i n g u l a r s → ω n:L{\text -}Singulars \to \omega such that if M M is an inner model not containing 0 # 0^\# : For some k , M ⊨ { α | n ( α ) ≤ k } k, M \models \{\alpha |n(\alpha )\leq k\} is stationary. For each k k there is a generic extension of M M in which 0 # 0^\# does not exist and { α | n ( α ) ≤ k } \{\alpha |n(\alpha )\leq k\} is non-stationary. This result is then applied to show that if M M is an inner model without 0 # 0^\#