论文标题
$π^1_1 \！ \！ \ downarrow $löwenheim-skolem-tarski固定逻辑的财产
The $Π^1_1 \! \! \downarrow$ Löwenheim-Skolem-Tarski property of Stationary Logic
论文作者
论文摘要
fuchino-maschio-sakai〜 \ cite {fuchinoetal_drp_lst}证明，固定逻辑的löwenheim-skolem-tarski（lst）属性等于对角上的反射原则，在内部俱乐部上（$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ fext} \ cite {drp}。我们证明，LST属性限制$π^1_1 $公式的（向下）反射，我们称之为$π^1_1 \！ \！ \ downarrow $ -lst属性等效于\ cite {cox_rp_is}的\ emph {internal}版本。结合\ cite {cox_rp_is}的结果，这表明$π^1_1 \！ \！ \ downarrow $ -lst的固定逻辑属性严格比固定逻辑的完整lst属性弱，尽管如果CH持有，则它们是等效的。
Fuchino-Maschio-Sakai~\cite{FuchinoEtAl_DRP_LST} proved that the Löwenheim-Skolem-Tarski (LST) property of Stationary Logic is equivalent to the Diagonal Reflection Principle on internally club sets ($\text{DRP}_{\text{IC}}$) introduced in \cite{DRP}. We prove that the restriction of the LST property to (downward) reflection of $Π^1_1$ formulas, which we call the $Π^1_1 \! \! \downarrow$-LST property, is equivalent to the \emph{internal} version of DRP from \cite{Cox_RP_IS}. Combined with results from \cite{Cox_RP_IS}, this shows that the $Π^1_1 \! \! \downarrow$-LST Property for Stationary Logic is strictly weaker than the full LST Property for Stationary Logic, though if CH holds they are equivalent.
