Timeline for What is the general opinion on the Generalized Continuum Hypothesis?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 20, 2011 at 16:29 | comment | added | Justin Moore | Also, another goal of set theory is also to develop a modest number of extensions of the axioms of ZFC which are sufficient to settle most questions which ZFC leaves unresolved. So even if a non set theorist asks "the wrong question" --- something which ends up being independent of ZFC, there is at least an apparatus in place to settle the question, even if this means showing it is independent. | |
| Feb 20, 2011 at 16:28 | comment | added | Justin Moore | I think many people working in set theory would agree that it is better to prove something in ZFC than to prove an independence result. But in many cases, proving an independence result is helpful in formulating ZFC theorems and proving them. Shelah has certainly made statements to this effect. Also, is it better to prove a consistency result classifying a collection of mathematical structures or to prove that a mess of counterexamples exists in ZFC? | |
| Feb 20, 2011 at 16:25 | comment | added | Justin Moore | Who said there isn't a "God given" model of set theory? We know ZFC doesn't axiomatize it (and that we'll never be able to). But that doesn't mean there isn't such a thing and that we can't attempt to discover its properties. | |
| Feb 6, 2010 at 21:25 | history | answered | John Goodrick | CC BY-SA 2.5 |