Tagging - 2016-10-10

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5:12 AM

Q: What about a separate tag for well-ordered sets? Or should it be synonym of (ordinals)?

There are many questions about well-ordered sets on the main and I consider well-orders to be an important topic. So perhaps they could deserve their own tag. On the other hand, many questions about well-orders are at the same time questions about ordinals so tagging them by both ordinals and (w...

It would fit, for example, here:

Q: Does well-ordering of the proper class of cardinal numbers imply choice?

It is well-known (forgive the pun) that the axiom of choice (which states that the product of every non-empty family of non-empty sets is non-empty) implies that the proper class of all cardinal numbers is well-ordered, at least in the presence of the ZF axioms. Does the converse hold? If not, i...