Forcing Axioms and the Definabilty of the Nonstationary Ideal on $\omega_1$

Autor:	Hoffelner, Stefan, Larson, Paul, Schindler, Ralf, Wu, Liuzhen
Rok vydání:	2022
Předmět:	Mathematics - Logic 03E35 03E45 03E47 03E55 03E57
Druh dokumentu:	Working Paper
Popis:	We show that under $\BMM$ and "there exists a Woodin cardinal$"$, the nonstationary ideal on $\omega_1$ can not be defined by a $\Sigma_1$ formula with parameter $A \subset \omega_1$. We show that the same conclusion holds under the assumption of Woodin's $(\ast)$-axiom. We further show that there are universes where $\BPFA$ holds and $\NS$ is $\Sigma_1(\omega_1)$-definable. Last we show that if the canonical inner model with one Woodin cardinal $M_1$ exists, there is a universe where $\NS$ is saturated, $\Sigma_1(\omega_1)$-definable and $\MA$ holds. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.05288 Zobrazit plný text záznamu View this record from Arxiv