Can I continue to use my current public server with CI 3.0?

I've just run phpinfo on the public server I use. It has PHP version 5.2.17, with MySQL version 5.0.51a

According to the version 3.0 change log, I will need MySQL 5.1

Can I use Codeigniter 3 with this particular server regardless, or am I stuck with version 2? (I may not be able to change hosting companies). I don't think I can get them to upgrade if other apps from other companies running on their servers require MySQL 5.0 (I will need to check. They are pretty flexible)

It may or may not work - no guarantees. Either way, I strongly encourage you to upgrade your environment.

CI may try to support PHP 5.2, but even that is discouraged.