论文标题
可确定类别类别的弱vopěnka原理
The Weak Vopěnka Principle for definable classes of structures
论文作者
论文摘要
根据其定义的复杂性，我们对弱vopěnka原理（WVP）进行了逐级分析，我们确定了每个级别的大型强度。因此，特别是我们表明，对于$σ_2$ - 可定义的类别的WVP等同于存在强的红衣主教。主要定理更普遍地表明，$σ_n$ - 可定义类的WVP等于存在$σ_n$ -strong Cardinal。因此，WVP等于存在$σ_n$ -strong Cardinal，所有$ n <ω$。
We give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures (WVP), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular we show that WVP for $Σ_2$-definable classes is equivalent to the existence of a strong cardinal. The main theorem shows, more generally, that WVP for $Σ_n$-definable classes is equivalent to the existence of a $Σ_n$-strong cardinal. Hence, WVP is equivalent to the existence of a $Σ_n$-strong cardinal, all $n <ω$.
