Java does not appear in the list of usable programs. I tried using the 'find programs online' button but it spit out an error (in a GUI text box):

GDBus.Error:org.freedesktop.DBus.Python.xdg.Except ions.ParsingError: Traceback (most recent call last):
File "/usr/lib/python2.7/dist-packages/defer/", line 489, in _inline_callbacks
result = gen.send(result)
File "/usr/lib/python2.7/dist-packages/sessioninstaller/", line 1030, in _install_mime_types
File "/usr/lib/python2.7/dist-packages/xdg/", line 33, in __init__
File "/usr/lib/python2.7/dist-packages/xdg/", line 42, in parse
IniFile.parse(self, file, ["Desktop Entry", "KDE Desktop Entry"])
File "/usr/lib/python2.7/dist-packages/xdg/", line 81, in parse
raise ParsingError("Invalid line: " + line, filename)
ParsingError: ParsingError in file '/usr/share/app-install/desktop/workrave:workrave.desktop', Invalid line: - RSI (Repetitive Strain Injury) oraz wspomaga rekonwalescencj\u0119

I'll note that I just wiped my hard drive and installed Ubuntu 13.04 a few weeks ago. I update as updates are supplied.
I installed JDK 7 using the software center.