Projective Wellorders and the Nonstationary Ideal

2016/10/13 by Stefan Hoffelner, Hoffelner, Stefan
Psychology · #FOS: Mathematics #Logic (math.LO) #Psychological Testing and Assessment

paper · pdf · doi:10.48550/arxiv.1610.04039

openalex publication_date 2016/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, under the assumption of the existence of M₁^#, there exists a model on which the restricted nonstationary ideal \hboxNS \upharpoonright A is ℵ₂-saturated, for A a stationary co-stationary subset of ω₁, while the full nonstationary ideal \hboxNS can be made Δ₁ definable with K_ω1 as a parameter. Further we show, again under the assumption of the existence of M₁^# that there is a model of set theory such that \hboxNS is ℵ₂-saturated and such that there is lightface Σ¹₄-definable well-order on the reals. This result is optimal in the presence of a measurable cardinal.

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