论文标题
强迫公理和非平稳理想的复杂性
Forcing axioms and the complexity of non-stationary ideals
论文作者
论文摘要
我们研究强迫公理对非平稳理想对$ω_2$复杂性的影响及其对某些联合性的限制。我们的主要结果表明，Martin最大值的加强$ mm^{++} $并未决定$ω_2$对非平稳理想的限制是否限制为$Δ_1$ -DEVINALITY的列为列出的序列是$Δ_1$ -DEFINALIDE，该公式在$ h（ω_3）$中的commulas in formulas in Formulas。在此结果证明中开发的技术还使我们能够证明$ω_2$的整个非平稳理想以及与CH兼容的强迫公理的结果。最后，我们通过证明$δ_1$ - 可定义在$ω_2$上的$δ_1$可定义性与$ω_2$的$δ_1$可定义性与任意的continuum continuum功能（$ω_2$）兼容。
We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on $ω_2$ and its restrictions to certain cofinalities. Our main result shows that the strengthening $MM^{++}$ of Martin's Maximum does not decide whether the restriction of the non-stationary ideal on $ω_2$ to sets of ordinals of countable cofinality is $Δ_1$-definable by formulas with parameters in $H(ω_3)$. The techniques developed in the proof of this result also allow us to prove analogous results for the full non-stationary ideal on $ω_2$ and strong forcing axioms that are compatible with CH. Finally, we answer a question of S. Friedman, Wu and Zdomskyyshow by showing that the $Δ_1$-definability of the non-stationary ideal on $ω_2$ is compatible with arbitrary large values of the continuum function at $ω_2$.
