17
votes
5answers
613 views

Why hasn't GCH become a standard axiom of ZFC?

I've never seen a text that includes GCH in the ZFC axioms. I presume this means that GCH has not achieved widespread acceptance. This seems surprising to me, given that: The cardinal numbers ...
2
votes
2answers
136 views

Forcing Question about a sequence of functions from $\aleph_{0}$ into $2 = \{0, 1\}$

I'm trying to go through Timothy Chow's A Beginner's Guide to Forcing (arxiv pdf). My particular question is about the first paragraph of Section $5$ (on p. $7$ of the above pdf). First, my vague ...
1
vote
3answers
45 views

Is this definition true about comparisons of sets?

I'm trying to find the error in a proof that yields a contradictory result, and I'm beginning to think that one of the definitions I start with is incorrect or self-contradictory. Is the following ...
3
votes
3answers
174 views

An elementary question regarding the uniqueness of a set, viewed with different cardinality

Does the cardinality of sets, like for example the real numbers, depend on the fundamental axioms one is working with? If so, what does it mean to speak of such a set if it is not really one single ...