Talk:Proper forcing axiom

Notation question
$$ [\lambda]^\omega $$ Am I correct that this is the power set of $$\lambda$$ restricted to subsets that are countable (of size $$\omega$$).? Thanks! Zero sharp 05:27, 25 October 2007 (UTC)
 * Basically. Sometimes it's taken to mean the set of all strictly increasing functions from &omega; to &lambda;, but it comes to the same thing. I'm a little surprised to see the notation in this context; I would have expected more $$P_{\omega_1}(\lambda)$$, which means exactly "countable (including finite) subsets of &lambda;". --Trovatore 23:51, 25 October 2007 (UTC)
 * Whoops, my bad; it doesn't come to the same thing. Of course not every countable subset of &lambda; is the range of an increasing function from &omega;. I think this should be examined to see which version is actually meant here. I sort of suspect the version with $$P_{\omega_1}(\lambda)$$ is more standard. --Trovatore 23:58, 25 October 2007 (UTC)

History and Formulation
There should be a history section, explaining that Proper Forcing was developed by Saharon Shelah. Set theorist (talk) 04:30, 17 June 2010 (UTC)
 * Yes, there should. Do you work in proper forcing?  Maybe you could add it.  I know just a little about it.  If you're new to WP, just write what you can (hopefully giving references); someone else can clean it up into WP style. --Trovatore (talk) 04:36, 17 June 2010 (UTC)