No start volume. set partition table to 'default' manually?

Hello,

I was installing Ubuntu for dualboot usage with El Capitan. The installation aborted; after reboot I couldn´t go back to OS X start volume, as if there was nothing installed. Recovery mode (CMD + R) is possible. Booting with Live-Ubuntu stick is also possible, there the data structure on the Mac partition is also visible, so it should still be there. 'First Aid' in Disk Utility tells me that something is wrong with the partition table, what may cause troubles with the start volume...
So, is there a possibility to manually correct the partition table (without testdisk) in the recovery mode to be able to start from OS X again? I´d like to avoid re-install it, since all data and software so far seems still to be there and ok - just setting back the partition table.

Thanks!