弱伏普尼卡原理并不意味着伏普尼卡原理
Weak Vopěnka's Principle does not imply Vopěnka's Principle
摘要：
Vopnka原理是说图的范畴没有大的离散的满子范畴，或者等价地说序数的范畴不能完全嵌入到图的范畴中。弱Vopnka原理是对偶命题，它说序数的相反范畴不能完全嵌入到图的范畴中。1988年，Adámek、Rosickelo和Trnková提出了这一概念，他们证明了这一概念是从伏波尼卡原理推导出来的，并询问这两个陈述是否等价。我们证明他们不是。然而，我们证明了弱Voppennka原理等价于其自身的推广，称为半弱Voppennka原理。
英文摘要：
Vopěnka's Principle says that the category of graphs has no large discrete full subcategory, or equivalently that the category of ordinals cannot be fully embedded into it. Weak Vopěnka's Principle is the dual statement, which says that the opposite category of ordinals cannot be fully embedded into the category of graphs. It was introduced in 1988 by Adámek, Rosický, and Trnková, who showed that it follows from Vopěnka's Principle and asked whether the two statements are equivalent. We show that they are not. However, we show that Weak Vopěnka's Principle is equivalent to the generalization of itself known as Semi-Weak Vopěnka's Principle.
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