A Failure of Π¹_n+3-Reduction in the Presence of Σ¹_n+3-Separation

2023/12/05 by Hoffelner, Stefan
#03E15 #03E35 #03E45 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2312.02540

Abstract

We show that one can force over L that Σ¹₃-separation holds, while Π¹₃-reduction fails, thus separating these two principles for the first time. The construction can be lifted to canonical inner models M_n with n-many Woodin cardinals, yielding that assuming the existence of M_n, Σ¹_n+3-separation can hold, yet Π¹_n+3-reduction fails.

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