The version numbers of the MyFaces Core project are on par with the JSF versions. That means MyFaces 1.2 is based on JSF 1.2. The MyFaces team is already working on MyFaces Core 2.0, which is based on JSF 2.0. Recently, a second beta version was released, see the announcements on the MyFaces homepage or the mailing list for the latest news.
MyFaces Core is just an implementation of the JSF standard. That means MyFaces Core 1.2 doesn't have AJAX functionality incorporated. The JSF 2.0 standard defines AJAX functionality, so MyFaces Core 2.0 does have AJAX functionality. That doesn't mean you can't have AJAX functionality when using MyFaces Core 1.2. Apart from the Core project, several sub projects of MyFaces exist that have JSF components with embedded AJAX functionality. Take a look at the Trinidad and Tomahawk projects for example. Both have AJAX enabled components and can be used on JSF 1.2. My book has chapters that cover the most important components of both sub projects and how to use their AJAX functionalities. The Trinidad project has already released an alpha version of their JSF 2.0 component set.