Weak Vopěnka's Principle does not imply Vopěnka's Principle
Abstract
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 SemiWeak Vopěnka's Principle.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.09333
 Bibcode:
 2019arXiv190909333W
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Logic
 EPrint:
 8 pages