Geodesic Curves Covering Surfaces

[SW VandeCarr]

The version on Wikipedia doesn't put a limitation on how many countable subsets you use.

Anyways, I don't think validity is the question you wanted to ask; it's not a theorem of ZFC, it's invalid in any model of ZFC+CH, and valid in any model of ZFC+AX.

I was content with maze's response -- I asked, and he answered, I didn't feel it important to press on. But my main reaction is simply that the criterion seems esoteric; it doesn't appear to obviously boil down to anything that I can imagine people having strong opinions about.

If AX were accepted, it would be a refutation of CH. People might have strong opinions about that. Should AX be rejected because it's 'esoteric'?

 

[Hurkyl]

I never said it should. Being esoteric just makes it hard to have opinions about.

The only times I've ever really ran into the CH are:
1. It let's you use $\aleph_1$ to refer to |R|
2. It simplifies the classification of real closed fields

Point (1) is highly superficial, and I don't work with real closed fields enough to have any string opinions about point (2). While AX is also related to CH, I have much less connection to it than these other two points.